There are provided a grinding machine and a grinding method that make it possible to achieve a high degree of accuracy of the roundness of a workpiece (W). As at least one of a coolant dynamic pressure Fp and a grinding efficiency Z varies depending on a phase ¸ of the workpiece (W), a pressing force F(¸) in the cut-in direction, which an eccentric cylindrical portion (Wa) of the workpiece (W) receives from a grinding wheel (15), varies and a degree µ(¸) of deflection of the eccentric cylindrical portion (Wa) also varies. In the grinding machine, the degree µ(¸) of deflection during grinding is acquired based on the coolant dynamic pressure Fp and the grinding efficiency Z, a first correction value D1(¸) for a command position of the grinding wheel (15) relative to the eccentric cylindrical portion (Wa) is computed, and the command position is corrected based on the first correction value D1(¸).
