The mechanical, electronic and optical properties of KH under high pressure have been studied using the generalized gradient approximation and Heyd-Scuseria-Ernzerh of hybrid method within density functional theory. Based on the usual condition of equal enthalpies, high pressure phase transition of KH from B1 to B2 was confirmed, is about 4.1 GPa, and normalized volume collapse ΔVP/V0 is about 11.09%. The calculated equilibrium structural parameters and elastic modulus are in excellent agreement with the experimental and other theoretical results. At ground states, B1 KH is elastic stable, but B2 KH is unstable. C11 and c′ are the main factors, which cause the structural phase transition under the pressures. The band structures and density of states of KH were calculated and analyzed in detail. Valance bands are local and conduction bands are continuous. The VBs mainly originate from K 3s, 3p and H 1s states, and the CBs consist of K 3s, 3p states, some hybridized levels are found between K 3s and 3p states. Mulliken population analysis of KH indicate that the charge populations of H 1s and K 3p states are very obvious but K 3s states are relatively weak, the charge transfers are from K to H. The linear response optical properties of KH were emphatically predicted combing with the band structures and frequency-dependent and dielectric function ε(ω).