Security is one of the most important aspects of the Internet of Things (IoT) due to the increasing trend of attacks in an IoT environment. Cryptographic techniques can be used to improve the security aspects of IoT implementation. Due to the limitations of computing resources in most devices connected to the IoT, reliable and efficient hash functions are required. In this paper, TWISH, a new hash design that can be efficiently implemented without compromising the security, is proposed. TWISH is based on the lightweight block cipher TWINE using the Davies-Meyer (DM) scheme. We analyze the security and randomness of the resulting output using the Cryptographic Randomness Test package. These tests include the Strict Avalanche Criterion (SAC), Collision, Coverage, and Linear Span test. The results show that TWISH can pass the applied tests. The tests also indirectly demonstrate that TWISH is quite resistant to near-collision, preimage, and differential/linear attacks.