Since their first demonstration in 2001 [Gol’tsman et al., Appl. Phys. Lett. 79, 705-707 (2001)], superconducting-nanowire single-photon detectors (SNSPDs) have witnessed two decades of great developments. SNSPDs are the detector of choice in most modern quantum optics experiments and are slowly finding their way into other photon-starved fields of optics. Until now, however, in nearly all experiments, SNSPDs were used as “binary” detectors, meaning that they could only distinguish between 0 and > = 1 photons, and photon number information was lost. Recent research has demonstrated proof-of-principle photon-number resolution (PNR) SNSPDs counting 2-5 photons. The photon-number-resolving capability is highly demanded in various quantum-optics experiments, including Hong-Ou-Mandel interference, photonic quantum computing, quantum communication, and non-Gaussian quantum state preparation. In particular, PNR detectors at the wavelength range of 850-950 nm are of great interest due to the availability of high-quality semiconductor quantum dots (QDs) [Heindel et al., Adv. Opt. Photonics 15, 613-738 (2023)] and high-performance cesium-based quantum memories [Ma et al., J. Opt. 19, 043001 (2017)]. In this paper, we demonstrate NbTiN-based SNSPDs with >94% system detection efficiency, sub-11 ps timing jitter for one photon, and sub-7 ps for 2 photons. More importantly, our detectors resolve up to 7 photons using conventional cryogenic electric readout circuitry. Through theoretical analysis, we show that the PNR performance of demonstrated detectors can be further improved by enhancing the signal-to-noise ratio and bandwidth of our readout circuitry. Our results are promising for the future of optical quantum computing and quantum communication.