In this work, we present the first principles calculations for structural, electronic and optical properties of perovskites CaZrO3 and CaHfO3 using the full-potential linearized augmented plane wave method (FP-LAPW) within the framework of density functional theory (DFT) as implemented in WIEN2k package. The exchange-correlation potential is treated with local density approximation (LDA) and generalized gradient approximation (GGA-PBE and PBESol). Additionally, the Tran Blaha modified Becke-Johnson exchange potential (mBJ) also is employed for electronic and optical calculations due to that it gives very accurate band gap of solids. Our obtained structural parameters are in good agreement with experimental datas and other theoretical results. The energy band gap obtained with mBJ is 4.56 eV for CaZrO3 and 5.27 eV for CaHfO3. The hybridization of states of O atom with those of Zr and Hf atoms in CaZrO3 and CaHfO3, respectively, is observed. The spin-orbit coupling effect on electronic properties of considered compounds also is investigated. Finally, the linear optical properties of CaZrO3 and CaHfO3 are derived from their complex dielectric function calculated with mBJ potential for wide energy range up to 45 eV, and all of them analyzed in details.