Technology computer-aided design (TCAD) of semiconductor devices relies on the numerical solution of differential equations in devices. Recent advances in quantum computing provide a new opportunity for TCAD simulations to be performed on a quantum computer. Based on a variational quantum algorithm, we develop a quantum-computing-based method to solve quantum confinement problems in semiconductor nanostructures. As the number of numerical discretization grid points for solving the Schrödinger equation increases, the number of qubits needed scales only logarithmically, ~ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${O}[\log(N)]$ </tex-math></inline-formula> . The method is applied to solve quantum confinement problems at all dimensions, which are related to confinement in a quantum well, semiconductor nanowire, and semiconductor quantum dot structures. The method can treat an anisotropic band structure and electrostatic potential in semiconductor nanostructures. We further show that the design of ansatz plays an important role in the performance of the method in terms of solution accuracy. The quantum-computing-based method can compute the energies and wave functions of both the ground and excited states with high accuracy.