We demonstrate multiphoton discrimination at a telecommunications wavelength with the readout frequency of 40 Hz by a charge-integration photon detector (CIPD). The CIPD consists of an InGaAs pin photodiode and a GaAs junction field effect transistor as a preamplifier in a charge-integration circuit, which is cooled to 4.2 K to reduce thermal noise. The quantum efficiency of the CIPD (the detector itself) is 80% for 1530 nm light, and the readout noise is measured as 0.26 electrons at 40 Hz. We can construct Poisson distributions of photocarrier numbers with distinct peaks at each photocarrier number, corresponding to a signal-to-noise ratio of about 3.