An Active Magnetic Regenerator (AMR) cycle that employs magnetocaloric materials (MCMs) as regenerators is generally used to realize the effective temperature span for magnetocaloric heat pump systems. The function of the magnetocaloric heat pump with the AMR cycle is based on the magnetocaloric effect (MCE) of an MCM. The MCMs of the first-order phase transition materials have gained attention because of the latent heat involved in their phase transitions. However, because the range within which the MCM exhibits an MCE is narrow near its Curie temperature, only a narrow temperature span exists in the case of the AMR with a single MCM. Therefore, there is a demand for an AMR system with material layers made of a couple of MCMs. However, only few studies have investigated the influence of the properties of MCMs on magnetocaloric heat pumps using material-layered systems. In the present study, the refrigeration capacity and the temperature span of the magnetocaloric heat pump with a material-layered bed of manganese-based compounds, which are first-order phase transition materials, were determined. It was found that the temperature span can be extended by optimizing the volumetric flow rate and the number of the layers that constitute the AMR. In addition, the number of the layers and the refrigeration capacity were found to be related.