To realize a biometric system with high security and good user acceptance, a multispectral palm vein image acquisition device based on an open environment was designed, and a palm vein recognition algorithm based on double constraints of principal component analysis (PCA) and least squares regression (LSR) was studied. In the process of least squares regression projection, the algorithm constrains the main element information extracted by principal component analysis, jointly driving the data and weakening the adverse effects of light scattering on recognition performance. It solves the problem of increased intra-class spacing caused by non-contact image acquisition. Experiments were conducted on palm vein databases of the Institute of Automation, Chinese Academy of Sciences, Tongji University, Hong Kong Polytechnic University, and the self-built, and the algorithm's lowest equal error rates were 0.72%, 0.50%, 0.18%, and 0.03%, and the correct recognition rates were 99.80%, 99.77%, 99.90%, and 99.95%, respectively. Compared with other typical methods, the system has advantages and practical application value.