Field-free switching of a perpendicularly magnetized ferromagnetic layer by spin-orbit torque (SOT) from the spin Hall effect is of great interest in the applications of magnetic memory devices. In this paper we investigate by micromagnetic simulations the possibility of deterministic field-free switching by combining SOT with the Dzyaloshinskii-Moriya interaction (DMI). We confirmed that within a certain range of DMI values and charge current densities, it is possible to deterministically switch the magnetization without the assistance of an external magnetic field. SOT terms including Slonczewski-like (damping-like) torque and field-like torque (FLT) are considered when analyzing the SOT switching and domain wall dynamics. We show that the FLT could play an adverse role in blocking and slowing down the magnetization switching under certain cases of DMI and charge current-driven field-free switching. However, in other cases, FLT assists DMI in the deterministic field-free SOT switching. In addition, it is found that FLT can effectively expand the current density window for deterministic field-free SOT switching in the presence of DMI.