Single-photon laser ranging has widespread applications in remote sensing and target recognition. However, highly sensitive light detection and ranging (lidar) has long been restricted in the visible or near-infrared bands. An appealing quest is to extend the operation wavelength into the mid-infrared (MIR) region, which calls for an infrared photon-counting system at high detection sensitivity and precise temporal resolution. Here, we devise and demonstrate an MIR upconversion lidar based on nonlinear asynchronous optical sampling. Specifically, the infrared probe is interrogated in a nonlinear crystal by a train of pump pulses at a slightly different repetition rate, which favors temporal optical scanning at a picosecond timing resolution and a kilohertz refreshing rate over $\sim 50\mathrm{ns}$. Moreover, the cross-correlation upconversion trace is temporally stretched by a factor of $2\times {10}^4$, which can thus be recorded by a low-bandwidth silicon detector. In combination with the time-correlated photon-counting technique, the achieved effective resolution is about two orders of magnitude better than the timing jitter of the detector itself, which facilitates a ranging precision of 4 μm under a low detected flux of $8\times {10}^{-5}$ photons per pulse. The presented MIR time-of-flight range finder is featured with single-photon sensitivity and high positioning resolution, which would be particularly useful in infrared sensing and imaging in photon-starved scenarios.