Abstract: We define new knot invariants, called colored Heegaard Floer homology for any knot K in the three sphere. This is the colimit of the cobordism maps from the (n, mn)-cable of K to (n, (m+1)n)-cable by letting m goes to infinity, which is invariant under full twists. We will describe the module structures of the colored Heegaard Floer homology and compute the colored Heegaard Floer homology for L-space knots.