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Public Key Cryptosystem (PKC) completely relies under the assumption that user's private key is absolutely secure. Exposure of private key may lead to disastrous situations in the communication network. To diminish the damage of private key exposure in PKC, key-insulation mechanism was introduced. In key-insulated cryptosystems, a user can update his private key with the help of a physically secure device from time to time. Identity-based cryptosystem alleviates the heavy certificate management problems in traditional PKC. Recently, many Identity-based key insulated signature schemes have been proposed in literature; however, most of the Identity-based schemes are designed based on the expensive bilinear pairing operation over elliptic curves. Due to the heavy computational cost of a pairing, the pairing based schemes are less efficient in practice. In order to improve the computational and communicational efficiency and to resist the problem of private key exposure in Identity-based signature schemes, we present a pairing-free key insulated signature scheme in identity based setting. We show that this scheme is unforgeable and achieves strong key insulation property with secure key updates, under the hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP). The performance analysis shows that our scheme is more efficient than the existing schemes. [ABSTRACT FROM AUTHOR]