• Mixed spin Ising model was proposed to describe two-dimensional Lieb-like lattice. • Influence of the periodically oscillating magnetic field on the magnetism of two-dimensional Lieb-like lattice have been investigated. • Multiple compensation temperatures were discovered. The phase diagram and magnetization of a two-dimensional Lieb-like lattice consisting of magnetic atoms with mixed spins 5/2, 3/2, and 2 were investigated based on the effective-field theory with correlations. They exhibited a compensation point below their phase transition temperatures, reentrant behavior, and depressed saturation magnetization within typical parameters of exchange couplings and anisotropies. In addition, the influence of a periodically oscillating magnetic field on the dynamic order parameters of a two-dimensional Lieb-like lattice is discussed. These results can help further understand two-dimensional materials' static and dynamic magnetic properties. Ising model of two-dimensional Lieb lattice is constructured and the Static and dynamic magnetic properties have been investigated for the system.