We have studied the field and spin dependences of the effective masses in CeIn3 as a function of pressure via the de Haas-van Alphen (dHvA) effect. The effective mass increases with the field at pressures up to about 10 kbar and then decreases with the field. The spin direction of the dominant dHvA oscillation is likely to be reversed across the same pressure. The dHvA frequency changes significantly at the pressure P(c) for the antiferromagnetic quantum critical point and two neighboring pressures P2 and P4 below and above P(c). The spin and field dependences rapidly diminish across P(c) and finally disappear above P4. These observations are discussed in conjunction with relevant observations and theories.