The authors have proposed constant envelope modulation (CEM) systems that enable to use a power-efficient nonlinear power amplifier on the transmitter side and a low resolution analog-to-digital converter (ADC) on the receiving side, where power consumption at the analog devices is effectively reduced by employing a low resolution ADC at the receiver. In such a receiver, the received signal is seriously affected by severe quantization error by the ADC and therefore BER performance is degraded. As a solution to performance degradation at the CEM receiver affected by quantization error, in this paper, we propose efficient nonlinear (Viterbi) equalization schemes that estimate both inter-symbol interference in multi-path channel and quantization error in ADC, where quantization error is estimated by using a simple function that models the relation between the received signal level and the resulting quantization error. In addition, the proposed scheme effectively reduces the number of states in Viterbi equalization to achieve computational complexity reduction for equalizations. Computer simulation results show that the proposed nonlinear equalization scheme improves BER performance of CEM receiver seriously affected by quantization error, while computational complexity is effectively reduced.