Ibn Rajab, may Allah have mercy on him, said:

“Fasting in Sha'baan is better than fasting in the Sacred Months*, and the best of voluntary fasts are those that are (observed in the months) closest to Ramadhaan, before or after. The status of these fasts is like that of al-Sunan al-Rawaatib which are done before and after Fardh (obligatory prayers) and which make up for any shortfall in the number of obligatory prayers. The same applies to fasts observed before and after Ramadhaan. Just as al-Sunan ar-Rawaatib are better than other kinds of voluntary prayers, so fasts observed (in the months) before and after Ramadhaan are better than fasts at other times.”

Reference: Lataa’if al-Ma’aarif fimaa li Mawaasim al-‘Aam min al-Wazaa’if, by Ibn Rajab al-Hanbali

Source: Islam QA, Article Title: The Month of Sha'baan

*Sacred Months: Zul Qa'dah, Zul Hijjah, Muharram, and Rajab (Saheeh Bukhari 3197)