We have designed and manufactured a reciprocating magnetic refrigerator (Carnot cycle) operating between 1.8K and 4.2K. The magnetic refrigerant was gadolinium gallium garnet (GGG). Operating tests were carried out varying maximum applied magnetic field Bm and operating frequency f. The experimental Bm and f dependence of useful cooling power showed good agreement with the calculated results. The maximum useful cooling power was 0.50W at 1.80K for Bm=3.0T and f=0.45Hz.