Silicon photomultipliers (SiPMs) constitute a promising candidate for photon-number-resolving (PNR) detection via spatial multiplexing, which offer advantages like high integration and low cost. Up to date, there has been continuous endeavor in boosting the PNR performances, particularly on the resolved photon numbers and operation speed. Here, we demonstrate a GHz-gated SiPM in the Geiger mode, which allows to quench the photon-induced avalanche signal within 1 ns. Specifically, the capacitive response of the SiPM has been effectively suppressed by combining the low-pass filtering and self-differencing technique, which facilitates a high-fidelity extraction of the avalanche pulse with a reduced error rate. Consequently, high-speed PNR detection has been manifested in resolving up to 14 photons for laser pulses at a repetition rate of 40 MHz. The presented high-speed PNR detector may open up new possibilities to implement applications such as large-dynamic-range optical sensing, high-capacity optical communication, and multi-photon quantum optics.