Yes, it is permissible for a person to do ‘Umrah before he does Hajj, because the Prophet (peace and blessings of Allaah be upon him) and his companions did ‘Umrah before they did the obligatory Hajj.
And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote.
Standing Committee for Academic Research and Issuing Fatwas
Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allaah ibn Ghadyaan, Shaykh ‘Abd-Allaah ibn Qa’ood.