We present the results of molecular dynamics simulations of the crystal nucleation rate in a supercooled Lennard-Jones liquid. The nucleation rate as a function of the pressure has been calculated by the method of determining the expectation time for liquid crystallization at temperatures higher than that of the triple point (T(*) = 0.865), close to the temperature of the terminal critical point of the metastable extension of the melting curve (T(*) = 0.55) and below this temperature (T(*) = 0.4). In computer experiments the nucleation rate varied from 10(32) to 10(35) s(-1) m(-3). The dimensions of critical nuclei and the pressure inside them, the surface free energy at a critical crystal nucleus-liquid interface, the height of the nucleation barrier, and the Zeldovich factor have been determined from the results of molecular dynamics simulations and their comparison with classical homogeneous nucleation theory. It is shown that the surface free energy at a curved crystal-liquid interface, as distinct from a flat interface, has also been determined at temperatures lower than the temperature of the terminal critical point of the melting curve and is a monotonically increasing function of the temperature.