We study phase structure and critical point of finite-temperature QCD in the heavy-quark region applying the hopping parameter expansion (HPE). We first study finite-size scaling on the critical point on $N_t=4$ lattices with large spatial volumes taking the leading order (LO) and the next-to-leading order (NLO) effects of the HPE, and find that the critical scaling of the Z(2) universality class expected around the critical point of two-flavor QCD is realized when the aspect ratio of the lattice is larger than about 9. This enables us to determine the critical point in the thermodynamic limit with high precisions. By a study of the convergence of the HPE, we confirm that the result of the critical point with the LO (NLO) approximation of the HPE is fairly accurate for $N_t=4$ (6), while we need to incorporate higher order effects for larger $N_t$. To extend the study to large $N_t$ lattices, we then develop a method to take the effects of higher-order terms of the HPE up to a sufficiently high order. We report on the status of our study on $N_t = 6$ lattice adopting the new method.