Using the full-potential linearized augmented plane-wave method based on the density functional theory, we investigate the influences of chemical substitution and uniaxial strain on the topological electronic structure of the half-Heusler compound LaPtBi. It is shown that the 8 band which is protected by the cubic symmetry of the C1b structure can open and form a gap by substituting Sc element for La or Pd for Pt in LaPtBi compound. However, in the case of distorting cubic lattice by using a uniaxial strain, not only the gap mentioned above appears, but also the Fermi level can be tuned regularly. Thus the LaPtBi compound becomes a real topological insulator.