Single-photon laser altimetry represents the future space-based lidar′s development trends. It has many advantages, such as high sensitivity, high repetition rate, light weight and small volume. For normal Gaussian echo signal, this work establishes the detection probablity model based on the lidar equation and the statistical property of single-photon detector. Then the quantitative relationship of ranging error is obtained. The model is simulated by Monte Carlo method. Results show that narrower pulse width can result in better accuracy and precision. Higher echo signal intensity can also lead to better precision, but it will bring about worse accuracy. Take the case of a Gaussian echo whose root-mean-square width is about 1.5 ns, when the mean number of signal photons is 1, the range accuracy is about 6 cm and the range precision is approximately 22 cm with a single shoot regardless of the noise.