We present a new InGaAs/InP Single-Photon Avalanche Diode (SPAD) with high detection efficiency and low noise, which has been employed in a sinusoidal-gated setup to achieve very low afterpulsing probability and high count rate. The new InGaAs/InP SPAD has lower noise compared to previous generations thanks to the improvement of Zinc diffusion conditions and the optimization of the vertical structure. A detector with 25 μm active-area diameter, operated in gated-mode with ON time of tens of nanoseconds, has a dark count rate of few kilo-counts per second at 225 K and 5 V of excess bias, 30% photon detection efficiency at 1550 nm and a timing jitter of less than 90 ps (FWHM) at 7 V of excess bias. In order to reduce significantly the afterpulsing probability, these detectors were operated with a sinusoidal gate at 1.3 GHz. The extremely short gate ON time (less than 200 ps) reduces the charge flowing through the junction, thus reducing the number of trapped carriers and, eventually, lowering the afterpulsing probability. The resulting detection system achieves a maximum count rate higher than 650 Mcount/s with an afterpulsing probability of about 1.5%, a photon detection efficiency greater than 30% at 1550 nm and a temporal resolution of less than 90 ps (FWHM).