We study the electron energy state for single and vertically coupled quantum dots (QDs). Our realistic three-dimensional (3D) modeling for narrow gap semiconductor QDs considers: (1) the effective one electronic band Hamiltonian; (2) the energy- and position-dependent electron effective mass approximation; (3) a finite height hard-wall confinement potential; and (4) the Ben Daniel-Duke boundary conditions. A robust nonlinear iterative algorithm is applied to solve the model for disk- (DI-) and conical- (CO-) shaped QDs. For single QD, we find that the most stable against the dot size deviations (between dots of the same base radius) is the electron energy spectra of the CO-shaped QDs. For vertically coupled QDs with the fixed dot size, the energy spectra can be controlled by an inter-dot distance between two dots. Due to weak interaction of wavefunctions, electron energies of the CO-shaped coupled QDs are less dependent on the inter-distance than that of the DI-shaped coupled QDs. This investigation is related to optical spectra and useful in optoelectronics applications.