Abstract: The study of glueballs is an important topic in hadron physics, and the search for glueball states is one of the major goal of the Beijing Spectrometer III(BESIII) experiment. Lattice quantum chromodynamics, as a first-principle approach to examine the non-perturbative characteristics of the strong interaction, is an essential theoretical tool to investigate the glueball problem. Recent development of lattice studies on glueballs and possible experimental candidates are reviewed in this article. In addition, the topological charge density of the gauge field can be used as an interpolation field operator to study the properties of pure-gauge pseudoscalar glueball, but only the contributions of the light pseudoscalar mesons \eta and \eta^\prime are observed in the correlation function of topological charge density operator on gauge configurations with dynamical sea quarks u, d and s. Our result implies that, in the presence of dynamical sea quarks, one needs to construct more different types of operators to study the pseudoscalar glueball.