In this paper, we propose a new version of the NTRU public key cryptosystem called CQTRU. It is a four-dimensional cryptosystem based on the commutative quaternion ring. This public key system has an ability to encrypt four sets of data in each session. Therefore, it gains the positive points and the strength of NTRU cryptosystems. The definition of the ring of CQTRU is introduced with the definition of its operations. The three phases of the new proposed system (key generation, encryption and decryption) are discussed in details, in addition to the decryption failure probability, key security and message security. Finally, the resistance of CQTRU's against lattice attack is investigated.