Abstract: In order to solve the problem of the high side lobe level in the circular array,a pattern synthesis method is proposed.It firstly makes the peak side lobe level as its fitness function to optimize the locations and coefficients of the array elements based on genetic algorithm,which is modified in order to avoid premature convergence.It accords with the academic global optimization and can greatly improve the algorithm search performance.Secondly,it makes the optimal results in the first step as a good initial iterative point and adopts Taylor approximation to transform the original pattern synthesis problem which is non-convex into sequential cone programming framework near the good initial point.After this it can be solved efficiently by the convex optimization.Due to the late variability capacity in the operation,it can effectively improve the optimization performance.Lastly simulations demonstrate that when the array number is constant,this method can not only reduce the side lobe level but also minimize its dynamic range.And it achieves a better performance of circular array pattern in comparison with the reference method.