Silicon single-photon detectors (SPDs) are key devices for detecting single photons in the visible wavelength range. Photon detection efficiency (PDE) is one of the most important parameters of silicon SPDs, and increasing PDE is highly required for many applications. Here, we present a practical approach to increase PDE of silicon SPD with a monolithic integrated circuit of active quenching and active reset (AQAR). The AQAR integrated circuit is specifically designed for thick silicon single-photon avalanche diode (SPAD) with high breakdown voltage (250-450 V), and then fabricated via the process of high-voltage 0.35-$mu$m bipolarCMOS-DMOS. The AQAR integrated circuit implements the maximum transition voltage of ~ 68 V with 30 ns quenching time and 10 ns reset time, which can easily boost PDE to the upper limit by regulating the excess bias up to a high enough level. By using the AQAR integrated circuit, we design and characterize two SPDs with the SPADs disassembled from commercial products of single-photon counting modules (SPCMs). Compared with the original SPCMs, the PDE values are increased from 68.3% to 73.7% and 69.5% to 75.1% at 785 nm, respectively, with moderate increases of dark count rate and afterpulse probability. Our approach can effectively improve the performance of the practical applications requiring silicon SPDs.