Public key encryption with equality test (PKEET) allows the testing of equality of underlying messages of two ciphertexts. PKEET is a potential candidate for many practical applications like efficient data management on encrypted databases. Identity-based encryption scheme with equality test (IBEET), which was introduced by Ma (Information Science 2016), can simplify the certificate management of PKEET. Potential applicability of IBEET leads to intensive research from its first instantiation. Ma’s IBEET and most of the constructions are proven secure in the random oracle model based on number-theoretic hardness assumptions which are vulnerable in the post-quantum era. Recently, Lee et al. (ePrint 2016) proposed a generic construction of IBEET schemes in the standard model and hence it is possible to yield the first instantiation of IBEET schemes based on lattices. Their method is to use a 3-level hierarchical identity-based encryption (HIBE) scheme together with a one-time signature scheme. In this paper, we propose, for the first time, a concrete construction of an IBEET scheme based on the hardness assumption of lattices in the standard model and compare the data sizes with the instantiation from Lee et al. (ePrint 2016). Further, we have modified our proposed IBEET to make it secure against insider attack.