Lattice QCD should allow quantitative predictions for the heavy quark physics from first principles. Up to now, however, most approaches have based on the nonrelativistic effective theory, with which the continuum limit cannot be taken. In this paper we investigate feasibility of relativistic approaches to the heavy quark physics in lattice QCD. We first examine validity of the idea that the use of the anisotropic lattice could be advantageous to control. the m(Q)a corrections. Our perturbative calculation, however, reveals that this is not true. We instead consider a relativistic O(a) improvement to handle heavy quarks on the isotropic lattice, which is eventually found to be the Fermilab quark action with a special choice of parameters. We explain how power corrections of m(Q)a can be avoided and remaining uncertainties are reduced to be of order (aLambda(QCD))(2).