The physical properties of the double-layer structure of graphyne-like described by the Ising model were studied by effective-field theory with correlations. The system is composed of mixed spin 5/2 and 2 with ferrimagnetic exchange couplings. The magnetization curve of the system can be divided into three types: P-, Q-, and N-types. Multiple compensation temperatures on the magnetization curve were found within a range of parameters. In addition, the influence of a periodically oscillating magnetic field on the magnetization of the double-layer structure of graphyne-like is discussed. The results indicated that the disorder and order of the system could be controlled and induced by a time-dependent and independent magnetic field.