The turbulent convection of liquid in a horizontal layer is simulated numerically for the case of heating from below. The liquid is assumed to be viscous and incompressible, and the layer boundaries are assumed to be flat, isothermal, and free from shear stress. The Boussinesq approach without any semi-empirical relationships (DNS) has been used and the flow is considered to be three-dimensional and non-stationary. The special pseudo-spectral method with resolution 65 3 of harmonics and Prandtl number equal to 10 is used. The present 3D,free simulation shows that exponent of power law at r ≥ 150 for temperature pulsations –2/15 coincides with the experimental result and that exponent of power laws for vertical velocity pulsations 0.4 and Reynolds number 0.5 are close to known experimental and numerical results. The same is also true for kinetic energy and rms velocity.