Praise be to Allaah.
There is no report from the Prophet (peace and blessings of Allaah be upon him) - as far as we know - to suggest that there is any particular virtue in performing Umrah in the month of Rajab, or that it is encouraged. Rather it is proven that there is a particular virtue in performing Umrah in the month of Ramadaan, and in the months of Hajj, which are Shawwaal, Dhu'l-Qa'dah and Dhu'l-Hijjah.
There is no report to prove that the Prophet (peace and blessings of Allaah be upon him) performed Umrah in Rajab, rather that was denied by Aa'ishah (may Allaah be pleased with her), who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) never performed Umrah in Rajab. Narrated by al-Bukhaari, 1776; Muslim, 1255.
Something that has been introduced into the religion is what some people do, namely singling out the month of Rajab for Umrah, because no one should single out a specific time for doing an act of worship unless that has been prescribed in sharee'ah.
Ibn al-Attaar, the student of al-Nawawi (may Allaah have mercy on them both) said:
What I have heard about the people of Makkah, may Allaah increase it in honour, is that they are accustomed to performing Umrah a great deal in Rajab. This is something for which I know of no basis, rather it is proven in the hadeeth that the Prophet (peace and blessings of Allaah be upon him) said: Umrah in Ramadaan is equivalent to Hajj. End quote.
Shaykh Muhammad ibn Ibraaheem (may Allaah have mercy on him) said in his Fataawa (6/131):
With regard to singling out some days of Rajab for any kinds of ziyaarah etc, there is no basis for that. Imam Abu Shaamah stated in his book al-Bida' wa'l-Hawaadith that performing acts of worship at specific times which were not prescribed by Islam is not right, because no time is better than any other, except times when it is prescribed to perform a certain kind of worship, or a time when all kinds of good deeds are better than at other times. Hence the scholars denounced the singling out of the month of Rajab for performing Umrah a great deal. End quote.
But if a person goes for Umrah during Rajab without believing that there is any special virtue in that, but it just so happens that it is easy for him to travel at that time, there is nothing wrong with that.