The development of a new public-key cryptosystem is discussed. This system is a hybrid combination of the RSA (Rivest-Shamir-Adleman) and knapsack crypto-systems. The message is encrypted in two stages using the knapsack algorithm followed by the RSA algorithm, and then decrypted in reverse order. The mathematics of the knapsack and RSA algorithms, a security analysis of the hybrid system, and a small computer simulation example are all included. The major advantages of this system, when compared with the knapsack and RSA crypto-systems, are higher speed and greater security.