The effects of both nanocrystal shape and applied magnetic field on the electron energy spectra of colloidal ZnO quantum dots have been investigated in the frame of finite element method, using nonuniform triangular elements. Four shapes of quantum dots (spherical, ellipsoidal, rod-shaped, and lens-shaped) were studied. It was found that the physical properties of the semiconductor quantum dots could be manipulated by changing their size and/or their shape. The energies of an electron increase as one reduces the quantum dot shape symmetry from spherical towards the lens-shaped. The magnetic field effect strongly interplays with the nanocrystal size and the nanocrystal shape effects. Such interplay has been attributed to the competition of the quantum confinement effect introduced by the barrier potential and the quantum confinement effect introduced by the applied magnetic field.