Much lately, a leveled fully homomorphic encryption scheme was proposed based on the Learning With Rounding (LWR) problem. The LWR problem is a variant of the Learning With Errors (LWE) problem, but it dispenses with the costly Gaussian noise sampling. Thus, compared with the existing LWE-based fully homomorphic encryption schemes, the proposed LWR-based fully homomorphic encryption scheme has much higher efficiency. But then, the user's evaluation key was needed to be obtained in the homomorphic evaluator of the proposed LWR-based fully homomorphic encryption scheme. Accordingly, a new leveled fully homomorphic encryption scheme was constructed based on the LWR problem, and the user's evaluation key was not needed to be obtained in the homomorphic evaluator of the new fully homomorphic encryption scheme. Since the new proposed fully homomorphic encryption scheme can be used to construct the schemes such as identity-based fully homomorphic encryption schemes, and attribute-based fully homomorphic encryption schemes, the new proposed scheme has wider application than the lately proposed LWR-based fully homomorphic encryption scheme.