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Every proton and neutron are made of elementary particles called quark. The dynamics of quarks is described by Quantum Chromo Dynamics (QCD) and it can be formulated on a structure lattice (Lattice QCD or simply LQCD). The bottle neck of LQCD simulation, which a Markov Chain Monte Carlo (MCMC), is solving large sparse linear equation. It appears in both generating configurations and calculating physical observables using configurations. In this talk, I will discuss linear solvers for LQCD application. I will mainly focus on our recent implementation of multigrid type solvers. I will also discuss usage of simd variables in LQCD.