This paper proposes a fast satellite screening algorithm aimed at the problem of balancing between positioning accuracy and system computing efficiency in a multi-constellation system environment under the Global Navigation Satellite System (GNSS). The algorithm constructs an observation model based on a positioning error for the larger number of satellites under a multi-constellation. The space region is divided based on elevation and azimuth angles to implement the screening algorithm for the solution of the point to be determined. An analysis of the experimental data shows that the average GDOP value of this scheme is 1.835, and the position error of the point to be determined is controlled within 2.5 m when the cut-off altitude angle is 5° and the screening ratio is more than 70%.