Starting from the quasiparticle random phase approximation based on the Skyrme interaction SLy5, we study the effects of phonon-phonon coupling (PPC) on the low-energy electric dipole response in 40−58 Ca. Using the same set of parameters we describe available experimental data for 40,44,48 Ca and give prediction for 50−58 Ca. The inclusion of the PPC results in the formation of low-energy 1 − states. There is an impact of the PPC effect on low-energy E1 strength of 40,44,48 Ca. The PPC effect on the electric dipole polarizability is discussed. We predict a strong increase of the summed E1 strength below 10 MeV, with increasing neutron number from 48 Ca till 58 Ca.