The unconstrained face images collected in the real environments are influenced by many complicated and changeable interference factors, and sparsity preserving projection cannot well characterize the low-dimensional discriminant structure embedded in the high-dimensional unconstrained face images, which is important for the subsequent recognition task. To solve this problem, we propose an effective dimensionality reduction method named as supervised sparsity preserving projections based on global constraint (SSPP-GC) which firstly enhances the reconstruction relationship of the same class of samples by adopting supervised over-complete dictionary and coefficient compactness constraints, and then appends the global constraint penalty in the step of the low-dimensional projection to further weaken the influence of other classes of samples. The experimental results on AR, Extended Yale B, LFW and PubFig databases demonstrate the effectiveness of the proposed approach.