Uthman ibn Hakim al-Ansari said: I asked Sa`id ibn Jubayr about fasting in Rajab, and we were then passing through the month of Rajab, whereupon he said: I heard Ibn `Abbas saying:
“The Messenger of Allah (may Allah bless him and grant him peace) used to observe fast so continuously that we thought he would not break it, and did not observe it so continuously that we thought he would not observe fast.”
*This hadith indicates that it is beneficial to fast in the month of Rajab and that the Messenger of Allah (may Allah bless him and grant him peace) would sometimes fast so continuously in this month that the companions thought he would fast continuously for the entire month. However, he would also sometime not fast, so much so that the companions thought that he would not observe any fasts in the month of Rajab. Having said this, the fact that the Messenger of Allah (may Allah bless him and grant him peace) fasted some of the time in Rajab makes it a virtuous Sunna to follow insha Allah.