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The structural and magnetic characteristics were studied for martensitic and austenitic Ni-Mn-Ga melt-spun ribbons of as quenched and as annealed at different temperatures. No essential structure change was found before and after annealing, but there are some anomalies in the magnetization process. In the austenite state the M͑T͒ curves measured in 100 Oe field exhibit a Hopkinson peak at T C for the ribbons of as quenched and annealed at 573 and 773 K, but the curves monotonically decays to zero with the increasing temperature to T C after annealing at 1073 K. In the martensite phase of both as quenched and 573 K annealed ribbons an abrupt increase in the slope of the M͑H͒ curve was observed; it appears to be due to the onset of magnetic-field-induced twin boundary motion. The abrupt slope change disappeared in the ribbons annealed at temperatures higher than 773 K. The ribbon processing history and particularly the quenched-in internal stress were modeled to probe the possible mechanisms for the anomalous magnetization behaviors, combining the grain-grain strain stored in the polycrystalline. The annealing temperatures were clarified into three groups according to their effects on the magnetization behaviors of the austenite and martensite.