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 are invariant under full twists. We will describe the module structures of the colored Heegaard Floer homology and show that the colimit is bounded in each gradings.