Fully Homomorphic Encryption (FHE) enables to evaluate arbitrary functions on encrypted data, where the noise to protect the security also results in the ciphertext expansion problem. Hybrid Homomorphic Encryption (HHE), also called transciphering, utilizes symmetric ciphers to address the expansion problem. But HHE also increases the transciphering computational costs on the server side. Therefore, how to design an efficient homomorphic decryption circuit plays a pivotal role for practical HHE. In the literature, researchers proposed several decryption circuits for block cipher SM4, which has been standardized for commercial cryptography in China. However, those proposals still have the practical issues about high latency, memory, and communication overhead. In this paper, we propose an HHE scheme with an improved functional bootstrapping of SM4, which reduces the time and memory costs for the ciphtertext transformation. Specifically, we construct homomorphic circuit for the lookup table (LUT) implementation of SM4, which are integrated from two homomorphic decryption circuits (Circuit 1 and 2). Circuit 1 follows the standard LUT implementation, whilst Circuit 2 optimizes the homomorphic evaluation. Compare to the bootstrapped version of Brakerski Gentry Vaikuntanathan (BGV) scheme of transciphering, the latency of Circuit 2 improves from 1.6 h to 285.5 s. The memory costs of our proposal are also reduced from 2 GB to 0.5 GB with respect to the Fully Homomorphic Encryption over the Torus (TFHE) scheme.