Sheikh Sayyed Sabiq states in his book Fiqh Us-Sunnah: According to the verdict of Ibn `Abbas and `Ikrimah if a person performs Hajj in fulfillment of a vow, while he has yet to perform the prescribed Hajj, then it should suffice him (and absolve him) from both. `Ata and Ibn `Umar, on the other hand, hold that one must first perform the Hajj obligatory on him, and thereafter perform another Hajj to fulfill his vow.
Given the above, it becomes clear that if the one who made a vow to perform Hajj has the means to perform Hajj twice (one in fulfillment of his vow and other for the obligatory Hajj), then he is to start with the obligatory Hajj. If he does not have the means to perform Hajj twice, he can perform Hajj once with double intention (in fulfillment of a vow along with the obligatory one).