Nowadays, the use of the Internet of Things has reached a commanding height in a new round of economic and technological upsurge. Its data transmission security has attracted much attention. It is well known that substitution permutation networks (SPNs) ciphers with high diffusion are not advantageous in unified encryption and decryption circuits with extremely resources constrained. Although some research has been carried out to address this issue, there are still insufficiencies. In this article, we propose a new 64-bit lightweight block cipher based on SPN named IVLBC, whose key allows 80 and 128 bits. The components of IVLBC are involutions. In particular, we propose a Feistel with tree structure to obtain a compact and involutive S-box. Also, the nibble-based involutive permutation is proposed to obtain the involutive permutation. Decryption can reuse encrypted code and circuitry in both software and hardware implementations. We prove that the costs of IVLBC are less than PRESENT, PRINCE, Midori, I-PRESENTTM, CRAFT, etc., in unified encryption and decryption circuits. In addition, we conduct other performance tests on IVLBC such as the differential attack, linear attack, integral attack, algebraic attack, invariant attacks, etc.