This paper presents an approximation quantum projection filtering strategy, aiming to reduce the computational cost in calculating the standard quantum filter equation in time. By using a differential geometric approach, the trajectory of the resulting quantum projection filter is constrained to evolve in a finite-dimensional differentiable manifold consisting of an exponential family of quantum density operators. A convenient design of the differentiable manifold is then developed through reduction of the local approximation errors, which allows simplification of the quantum projection filter equations. Finally, simulation results from a two-level quantum system example illustrate the approximation performance of the proposed filtering scheme. The proposed approach is expected to be of practical use in developing more efficient quantum control methods.