Background: Nuclear shell model is widely applied in the studies of light and medium-mass nuclei. The ground and excited state energies, electromagnetic properties and β decay properties of these nuclei can be well understood by solving many body Schrödinger equation with effective shell-model Hamiltonian in the model space. Purpose: The aim is to introduce the framework of shell model and its application in nuclei. Methods: The nuclear shell model is used to study properties of selected nuclei. Results: In psd region, a new effective shell-model Hamiltonian is introduced. The neutron drip-line of C, N, and O isotopes can be given with such Hamiltonian. The nuclei around A=20 with weakly bound proton are investigated through a modified shell model Hamiltonian. N=Z nucleus is good for studying the effect of proton-neutron pair. 46V and 50Mn have both T=0 and 1 rotational band. 92Pd can be understood under a spin alignment isoscalar scheme of proton-neutron pair. Mirror nuclei around N=Z in fp region can be used for the investigation of charge symmetry breaking effect of nuclear force. Conclusion: Nuclear shell model is proper and useful for the description of light and medium-mass nuclei.