Photonic time-stretch analog-to-digital converter (PTS-ADC) system utilizes the dispersion effect of fibers to stretch the sampled analog signal in time domain and compress its bandwidth in frequency domain, which can highly improve the sampling rate and bandwidth of the traditional analog-to-digital converter (ADC). Due to the time-aperture limitation, the traditional PTS-ADC is difficult to satisfy the continuous-time signal sampling. Multi-channel architecture is adopted to achieve a PTS-ADC operating in the continuous-time mode. However, this architecture introduces the inter-channel mismatch. A multi-channel architecture is optimized so as to achieve a continuous-time PTS-ADC system with improved accuracy. The effects of inter-channel offset, gain and time mismatches are studied by numerical simulation. A three-channel experimental system with the sampling rate of more than 200 GSa/s, bandwidth of 45 GHz, and effective number of bits (ENOB) of ~3.7 is domonstrated.