A blind carrier phase derotator can be employed to correct and track carrier phase offset either before or after equalization in a blind adaptive receiver. This work proposes a computationally efficient blind carrier offset recovery algorithm for 8-vestigial side-band (8-VSB) signals by designing its cost function such that its cost surface has only two global minima without any undesirable local minima. Consequently, the proposed algorithm is not complicated by the possibility of a stochastic gradient descent (SGD) algorithm converging to a false local minimum, and global convergence can always be ensured. Moreover, the proposed algorithm can adopt a large step size in the transient period to accelerate the convergence speed along with a small step size in the convergence period to reduce the stochastic gradient noise.