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The observed mass-to-light ($M/L$) ratios of a large sample of GCs in M31show an inverse trend with metallicity compared to what is expected from SimpleStellar Population (SSP) models with an invariant canonical stellar IMF, in thesense that the observed $M/L$ ratios decrease with increasing metallicity. Weshow that incorporating the effect of dynamical evolution the SSP models with acanonical IMF can not explain the decreasing $M/L$ ratios with increasingmetallicity for the M31 GCs. The recently derived top-heavy IMF as a functionof metallicity and embedded cluster density is proposed to explain the lowerthan expected $M/L$ ratios of metal-rich GCs. We find that the SSP models witha top-heavy IMF, retaining a metallicity- and cluster mass- dependent fractionof the remnants within the clusters, and taking standard dynamical evolutioninto account can successfully explain the observed $M/L-[Fe/H]$ relation of M31GCs. Thus we propose that the kinematical data of GCs can be used to constrainthe top-heaviness of the IMF in GCs.

A Possible Solution for the M/L-[Fe/H] Relation of Globular Clusters in M31: A metallicity and density dependent top-heavy IMF