Protecting secret keys is crucial for cryptography. There are some relatively insecure devices (smart cards, mobile phones etc.) which have threat of key exposure. The goal of the forward security is to protect security of past uses of key even if the current secret key is exposed. In this paper, the authors propose lattice based forward-secure identity based encryption scheme based on LWE assumption in random oracle model. They also propose lattice based forward-secure identity based encryption scheme in the standard model.