We consider some iterative methods of higher order for simultaneous determination of the polynomial zeros. The proposed methods are based on Euler’s third-order method for finding a zero of a given function and involve Weierstrass’ correction. We prove that the presented methods have the order of convergence equal to four or more. The accelerated convergence is obatined with negligible number of additional operations, so that these methods possess a very high computational efficiency. The convergence speed is illustrated on a numerical example.