We introduce a hybrid high-order method employing Nitsche's boundary penalty techniques for the Poisson problem on the curved and complicated domain. There are two key ideas in this work: Firstly, the methods employ the Nitsche-type boundary penalty technique to weakly enforce the boundary conditions, which avoids the computation of the parameterized mapping for the curved boundary. Secondly, an optimal L2 error estimate for the Poisson problem with mixed Dirichlet and Neumann boundary conditions is derived. Moreover, the stability and optimal error estimate for the proposed HHO methods are independent of the number and measure of faces on the domain boundary. Finally, a numerical experiment is presented in this chapter to confirm the theoretical results.