The horizontal convection at high Rayleigh number (Ra) in a rectangle cavity with aspect ratio of 1∶10 is numerically simulated. The horizontal convection is an important model to understand the ocean circulation and the power laws of the flow are the most concerned. According to the results within the regime of 104Ra11, three continuous regimes are obtained: the linear regime (104Ra6), the transition regime (106Ra8) and the 1/5-power law regime (108Ra11). For the flow strength, a 1/3-power law of Ra is fitted when Ra is not high enough (107Ra8). However, a 1/5-power law is obtained when Ra is high enough (108Ra11). The 1/5-power law confirms the analysis of Rossby and implies that 1/3-power law of Ra for Nusselt number by Siggers et al. is an over estimation.