At present, sparse arrays have been widely used in the field of underwater acoustic imaging. Aiming at the distribution characteristics of sparse array raising the sidelobe level, reducing the imaging contrast and other issues, a kind of underwater acoustic sensor array synthesis method based on convex optimization algorithm is proposed. On the basis of the appropriate object function, this method makes multiple iteration operations on the planar array, and optimizes the position of the array element and the element excitation. Finally, the planar array of 20×20 elements is optimally integrated into sparse array of 51 elements, the sidelobe lever is under －15 dB. By comparing the beam pattern performance based on convex optimization algorithm with the Chebyshev arrays synthesis method, the results show that the sparse array optimized in this study not only ensures the imaging quality, but also significantly reduces the number of array elements, and reduces sidelobe level. In addition, it decreases the complexity of the system and the design cost.