Coded-aided carrier synchronization can fully utilize the soft information of data symbols from the decoding process for carrier parameter estimation, demonstrating excellent performance under low Signal-to-Noise Ratio(SNR) conditions. Classical coded-aided carrier synchronization methods mainly solve nonlinear equations containing hidden variables through the Expectation-Maximization (EM) algorithm or its series expansion approximations, but suffer from high complexity or limited estimation accuracy. This paper exploits the characteristic that the Jacobian matrix of the log-likelihood function derivative in polar form is easy to derive, and uses the Newton-Raphson iterative algorithm to solve the nonlinear function. Under the condition of maintaining parameter estimation performance without degradation, the computational complexity of coded-aided carrier synchronization parameter estimation is significantly reduced. Computer simulations show that the proposed algorithm can achieve Bit Error Rate(BER) performance comparable to the EM algorithm while significantly reducing computational complexity, approaching that of series expansion approximation algorithms. It is applicable to single carrier linear modulation systems such as Binary Phase Shift Keying(BPSK), Quadrature Phase Shift Keying(QPSK), and Quadrature Amplitude Modulation(QAM).