Non-line-of-sight (NLOS) imaging enables monitoring around corners and is promising for diverse applications. The resolution of transient NLOS imaging is limited to a centimeter scale, mainly by the temporal resolution of the detectors. Here, we construct an up-conversion single-photon detector with a high temporal resolution of ∼ 1.4 ps and a low noise count rate of 5 counts per second (cps). Notably, the detector operates at room temperature, near-infrared wavelength. Using this detector, we demonstrate high-resolution and low-noise NLOS imaging. Our system can provide a 180 µm axial resolution and a 2 mm lateral resolution, which is more than one order of magnitude better than that in previous experiments. These results open avenues for high-resolution NLOS imaging techniques in relevant applications.