Pope St. Linus was bishop of Rome from around A.D. 66 to around A.D. 78. His name occurs in a number of early lists of Roman bishops (Irenaeus, Adversus Haereses 3.3.2; Eusebius, Historia Ecclesiastica 3.2, 3.4.8, 3.2.1, 5.6.1; and elsewhere), and we may thus safely assume that he actually existed. Both Eusebius and Irenaeus tell us that he is to be identified with the Linus whom Paul mentions in 2 Tim. 4:21 ("Make haste to come before winter. Eubulus and Pudens and Linus and Claudia and all the brethren, salute thee.") He was actually the first bishop of Rome, and not the second. Though Peter, his ostensible predecessor, may have founded a Christian community in Rome, tradition did not identify him as the city's first bishop until considerably later, at the end of the second century.

As modern scholars hasten to point out, it is very unclear what being a bishop of Rome in the first century of the common era actually constituted. The monarchical episcopate did not emerge until the second century; before then, local churches seem to have been governed by clerical comittees rather than by individual bishops.

The rather unreliable biography of Linus given in the Liber Pontificalis, or "Book of the Popes" is as follows (Latin text from the edition of L. Duchesne, Le Liber Pontificalis, Paris, 1955, vol. I, p. 121):

"Linus, natione Italus, regionis Tusciae, patre Herculano, sedit ann. XI m. III d. XII. Fuit autem temporibus Neronis, a consulato Saturnini et Scipionis usque ad Capitone et Rufo consulibus. Martyrio coronatur. Hic ex praecepto beati Petri constituit ut mulier in ecclesia velato capite introiret. Hic fecit ordinationes II, episcopos XV, presbiteros XVIII. Qui sepultus est iuxta corpus beati Petri, in Vaticano, sub die VIIII kal. octubris."

In English (my translation):
"Linus, Italian by birth, from the region of Tuscany, whose father was Herculanus, was pope for eleven years, three months, and twelve days. This was in the time of Nero, from the consulate of Saturninus and Scipionis (in A.D. 56) to that of Capito and Rufus (in A.D. 67). He was crowned a martyr. According to the precept of the blessed Peter, he established that women should enter churches with their heads veiled. He performed two ordinations, (consecrated) fifteen bishops and eighteen priests. He was buried next to the body of the blessed Peter, in the Vatican, on the ninth day before the Kalends of October (23 September)."