Q: Does performing ‘Umrah (lesser pilgrimage) during the months of Hajj have any particular virtue different from performing it in other months?
A: The best month to perform ‘Umrah is during Ramadan, for the Prophet (peace be upon him) said:
‘Umrah (performed) in Ramadan is equal to Hajj (in reward). 
(Agreed upon its authenticity by Imams Al-Bukhari and Muslim)
According to another narration by Al-Bukhari:
It is equivalent to performing Hajj with me. 
According to the narration by Muslim:
It is equivalent to Hajj or Hajj performed with me (in reward). 
This means that it is equivalent to Hajj or (indicative of uncertainty on the part of the Hadith narrator) equivalent to Hajj performed with the Prophet (peace be upon him).
Then, comes the ‘Umrah in Dhul-Qa‘dah, for all the ‘Umrahs which the Prophet (peace be upon him) performed took place in Dhul-Qa‘dah. Allah (Glorified be He) says:
Indeed in the Messenger of Allâh (Muhammad صلى الله عليه وسلم) you have a good example to follow 
May Allah grant us success!
 Narrated by Imam Ahmad, Section on the Hadiths narrated by Banu Hashim, the beginning of the Chapter on the Hadiths narrated by `Abdullah ibn `Abbas, no. 2804; and Ibn Majah, Book on rituals, Chapter on excellence of performing `Umrah in Ramadan, no. 2994.
 Narrated by Al-Bukhari, Book on Hajj, Chapter on Hajj for women, no. 1863.
 Narrated by Muslim, Book on Hajj, Chapter on excellence of performing `Umrah in Ramadan, no. 1256.
 Surah AlAhzab, 33: 21
Source: Fatwas of Ibn Baz
- Umrah in Ramadhan – If a traveller arrives in Makkah and he is fasting, should he break his fast? – Shaykh ibn Uthaymeen ( A very important read)