MOLLI is a well-known method for cardiac T1 mapping. Data sampling in MOLLI is based on SSFP readout. It is therefore susceptible to off-resonance which is considered an error source for T1 mapping. We have presented a method to suppress off-resonance variation error in T1 estimation by means of a specific CE-FAST in combination with MOLLI. We have evaluated our method in simulation and Phantom experiment with promising results.