A class of multimodulus algorithms (MMA(p)) optimized by an optimal step-size (OS) for blind equalization are firstly investigated in this letter. The multimodulus (MM) criterion is essentially a split cost function that separately implements the real and imaginary part of the signal, hence the phase can be recovered jointly with equalization. More importantly, the step-size leading to the minimum of the MM criterion along the search direction can be obtained algebraically among the roots of a higher-order polynomial at each iteration, thus a robust optimal step-size multimodulus algorithm (OS-MMA(p)) is developed. Experimental results demonstrate improved performance of the proposed algorithm in mitigating the inter-symbol interference (ISI) compared with the OS constant modulus algorithm (OS-CMA). Besides, the computational complexity can be reduced by the proposed OS-MMA(2) algorithm.