Biochar is widely used as a soil amendment. Enzyme activity is an important factor that reflects soil metabolic activity, and is involved in biochemical processes such as organic matter decomposition and nutrient cycling in soils. However, the effects of biochar prepared for different straw materials on soil enzyme activity and soil nutrients are rarely studied. Through pot experiments, the effects of different straw (wheat, rice, maize) biochars (obtained by pyrolysis at 500 °C) on soil organic carbon, nitrogen, available phosphorus, and enzyme activity were studied in paddy soil. The results showed that the addition of biochar increased the soil organic carbon content, which gradually decreased with the extension of the rice growth period. The soil ammonium nitrogen content gradually decreased as the rice growth period continued; however, the soil nitrate nitrogen content first decreased and then increased over the rice growth period. Soil invertase, phosphatase, and urease activity first increased and then decreased, and the enzyme activity was the highest at the heading stage of rice. At this time, there were also significant correlations between enzyme activity and carbon, nitrogen, and phosphorus levels, except in the case of soil urease activity. The geometric mean of the investigated enzyme activities was the highest after amendment with rice straw biochar. These results indicate that the response of enzyme activity to biochar depends on the biochar feedstock and the rice growth stage.