Low-resolution analog-to-digital converters (ADCs) may need to be implemented in a full-digital massive multi-user MIMO system for low-power consumption. In this paper, the performance with a proposed ADC design for low-resolution ADCs to suppress the amount of degradation due to the quantization process in the full-digital massive multi-user MIMO system is evaluated. In the proposed ADC design, quantization range limit is specified based on the mean amplitude of a received signal and the input amplitude is bounded to eliminate thermal noise. Numerical results show that, through clipping the thermal noise by setting the appropriate quantization range limit, the full-digital massive MIMO with low-resolution ADCs (even 1-bit ADCs) realizes better system throughput than that with infinite-resolution ADCs. It is also shown that the throughput with low-resolution ADCs is equivalent to that with infinite-resolution ADCs when the number of users is less than three (the number of streams is less than six).