A new dual-mode algorithm for blind equalization of quadrature amplitude modulation (QAM) signals is proposed. To solve the problem that the constant modulus algorithm (CMA) converges to the constellation with the arbitrary phase rotation, with the modification of the CMA, the proposed algorithm accomplishes blind equalization and carrier phase recovery simultaneously. In addition, the dual-mode algorithm combining the modified constant modulus algorithm (MCMA) with decision-directed (DD) algorithm achieves the performance enhancement of blind convergence speed and steady-state residual ISI. So we can refer the proposed algorithm to as a scheme for joint blind equalization and carrier phase recovery. Simulation results for i.i.d. input signals confirm that the dual-mode algorithm results in faster convergence speed, samller residual ISI, and better carrier phase recovery than those of the CMA and DD algorithm without any significant increase in computational complexity.