A high-precision time integrator is presented whose output is the accumulation of sequence of time inputs. A novel time adder with time-domain differential structure is proposed to avoid common-mode errors such as supply noise and leakage current. The performance under various process, voltage and temperature conditions is examined in detail. By using two time adders in parallel, a differential synchronous time integrator is proposed, which is easier to cascade with other time-mode arithmetic circuit. Implemented in 65 nm 1.2 V CMOS technology, the proposed time integrator achieves a gain of 27.97 dB with a 317 kHz 30 ps peak-to-peak sinusoidal input, and consumes with 50 MHz sampling rate. The experimental results confirm the integration operation is realised properly and accurately.