T1 relaxation time has been a valuable biomarker with emerging applications in cardiac diseases and liver function. Traditional inversion-recovery T1 quantification method is frequently applied as the reference for various T1 quantification methods. When applied in targets where fat and water signals co-exists, the single component fitting model would be in a dilemma. Combining the inversion-recovery T1 quantification with existing fat-water quantification methods, this work presented a solution for multi-component T1 quantification. Proposed method has been tested on fat-water phantoms and showed good consistency over a wide range of fat fractions.