Two-dimensional(2D) PtSe2 has the unique properties such as large-range tunability in band gap and high air stability, holding a great promise in the development of novel optoelectronic devices. In this work, the ultrafast photocarrier dynamics in 2D PtSe2 with different thicknesses have been studied by using time-resolved terahertz(THz) spectroscopy. It is found that both the amplitude of transient THz photoconductivity and its dependence on the excitation fluence of the material show a significant nonlinear increase with the increase of sample thickness. The dynamical parameters including photocarrier density, scattering time and backscattering factor are obtained through analyzing the THz frequency-dependent conductivities. In combination with the excitation-wavelength dependent THz relaxation dynamics, it can be inferred that the competition between bound excitons and free carriers is mainly responsible for the nonlinear thickness dependence. In addition, the exciton effect and thickness-induced semiconductor-semimetal transition in PtSe2 are also revealed using the optical pump-optical probe spectroscopy. This work demonstrates the effective regulation on the nonequilibrium ultrafast dynamics of PtSe2 through varying the thickness of materials, and provides an important guideline for the optoelectronic applications of noble-metal based 2D materials.