A hybrid numerical model of the magnetic refrigerator with multi-material microchannel regenerator has been developed. The magnetocaloric effect was implemented using instantaneous temperature rise/drop (discrete method). Two pipe-in-pipe heat exchangers at two ends of the regenerator were treated using ε-NTU method. The commercially available compounds of LaFe_13-x-yCo_xSi_y as well as hypothetical compounds of Gadolinium were considered as the magnetocaloric materials (MCMs) with different Curie temperatures. The predicted results of the present work for parallel-plate regenerators employing different compounds of LaFe_13-x-yCo_xSi_y were broadly in good agreement with the available experimental data. The cooling capacity increases as the number of MCMs increase. However, for a given length of regenerator, an optimum number of MCMs was seen yielding the maximum performance of the refrigerator. For a given number of MCMs, a smaller Curie temperature difference ΔT_Cu between the MCMs was found to give higher performance.