In this paper, a novel pulse-train time amplifier is proposed that achieves linear, accurate, and programmable gain for a wide input range. Using the proposed pulse-train time amplifier, a 7-bit two-step TDC is implemented. The proposed TDC employs repetitive pulses with gated delay-lines for a calibration-free and programmable time amplification and quantization. The prototype chip fabricated in 65 nm CMOS process achieves 3.75 ps of time resolution at 200 MS/s while consuming 3.6 mW and occupying 0.02 mm$^2$ area. Compared to previously reported TDCs, the proposed TDC achieves the fastest conversion rate and the best FoM without any calibration.