It is known as ‘The Gospel According to John’, and the ‘John’ in question is traditionally considered to have been the apostle, one of the Twelve.

But doubts have been raised about this, even by such relatively conservative scholars as Richard Bauckham.

An argument in favour of the traditional authorship was developed by B.F. Westcott.  William Hendriksen (New Testament Commentary) presents his own version of that argument:

According to the information furnished by the Gospel itself the author was:

(1) A Jew

a. This is evident from his style.

b. It also follows from his thorough acquaintance with the Old Testament, which he is able to quote both according to the Hebrew and from the Septuagint. See the following passages: Jn 2:17; 10:34, 35; 12:40; 13:18; 17:12; 19:24, 28, 36, 37.

c. It is corroborated by his references to Jewish (and Samaritan) religious beliefs, particularly regarding the Messiah: Jn 1:41, 46, 49; 4:25; 6:15; 7:27, 42; 12:34.

d. It is supported by evidence which indicates that the author is acquainted with religious and political conditions in Palestine: Jn 4:9; 7:35; 11:49; 18:13, 28, 31, 39; and also with Jewish feasts and purification-rites: the Passover: Jn 2:13, 23; 6:4; 13:1; 18:28; perhaps also 5:1; the Feast of Tabernacles: Jn 7:2, 37, 38; the Feast of Dedication: Jn 10:22, 23. See also Jn 3:25; 11:55; 12:12; 18:28, 39; 19:31.

e. It explains the easy and natural manner in which he introduces Jewish customs with reference to weddings and funerals: Jn 2:1–10; 11:38, 44; 19:40.

(2) A Palestinian Jew

He has a detailed knowledge of Palestinian topography: Jn 1:28 cf. 11:1; 2:1, 12; 3:23; 4:11, 20; 11:54; 12:21; particularly, of Jerusalem and its immediate vicinity: Jn 5:2; 9:7; 11:18; 18:1; 19:17; and of the Temple: Jn 2:14, 20; 8:2, 20; 10:22, 23; 18:1, 20.

(3) An eye-witness

As such he remembers when the events occurred; sometimes the exact hour: Jn 1:29, 35, 39; 2:1; 3:24; 4:6, 40, 52, 53; 6:22; 7:14; 11:6; 12:1; 13:1, 2; 19:14, 31; 20:1, 19, 26.

He knows that Jesus was weary when he sat down by the well (Jn 4:6); he remembers the very words spoken by the neighbors of the man born blind (Jn 9:8–10); he himself saw the blood and water issuing from the pierced side of Jesus (Jn 19:33–35); he knows by name the servant of the high priest whose right ear was cut off by Peter (Jn 18:10); and he is acquainted with the high priest (Jn 18:15). These and many other details clearly show that the author was an eye-witness of the events which he records.

(4) One of the Twelve

The fact that he partakes of the Supper with his Lord shows that he must be one of the Twelve (Jn 13:23). His close association with Peter would also seem to prove this (Jn 1:35–42; 13:23, 24; 18:15, 16; 20:2; 21:20–23). That the writer was, indeed, one of the apostles appears also from his intimate knowledge of their actions, words, and feelings: Jn 2:17, 22; 4:27; 6:19; 12:16; 13:22, 28; and 21:21. And if anyone should argue that it is not clear that in all these cases the disciples whose reactions are recorded belong to the inner group and that therefore the inference which we have drawn is not quite convincing, we call attention to such other passages where the reference is distinctly to “the twelve,” (Jn 6:66–71; 20:24–29). The author knows exactly what was said within that inner group! The conclusion is inescapable that he belongs to it.

Note also that in Jn 1:35–51 the unnamed disciple is mentioned in connection with Andrew, Simon Peter, Philip, and Nathanael, all of whom belong to the Twelve.

(5) The Apostle John.

This surely is the most natural inference to be drawn from all the facts presented. It is to be noted that the author, while mentioning other apostles by name, never indicates in that distinct manner either John or his brother James. That very fact is significant and would seem to point in the direction of the writer’s identity.