Summary: A new public-key cryptosystem is presented. This system is a multistage trapdoor knapsack cryptosystem. In this system the message is encrypted and decrypted in multistages using a knapsack algorithm. The knapsack algorithm, a security analysis of the multistage system, and a small computer simulation example are presented. The main advantage of the proposed system is that it provides higher security than a single-stage knapsack cryptosystem of the same length.