Partial decryption enables a ciphertext to be decrypted partially according to provided secret keys. In this paper, we propose a public key encryption scheme with the functionality of partial decryption. Our strategy is to use the NTRU cryptosystem. Under a design principle of the mathematical structure “group ring”, we extend the original NTRU into group ring NTRU (GR-NTRU). First, we propose a generic framework of our GR-NTRU. Our GR-NTRU allows partial decryption with a single encryption process using a single public key. Besides, when we execute partial decryption under a secret key of GR-NTRU, we need no information to identify each part in a whole ciphertext. Consequently, management of a public key and a corresponding set of secret keys is rather easier than the naive method. Next, we propose a concrete instantiation of our generic GR-NTRU. A multivariate polynomial ring NTRU scheme is obtained by employing a product of different cyclic groups as the basis of the group ring structure.We will show examples of those new variants of NTRU schemes with concrete parameter values, and explain how we can employ them to use the functionality of partial decryption.