Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of InAs quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped nano-dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs potential.