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The f-electron compound CeAuSb2, which crystallizes in the ZrCuSi2-type tetragonal structure, orders antiferromagnetically between 5 and 6.8 K, where the antiferromagnetic transition temperature T_N depends on the occupancy of the Au site. Here we report the electrical resistivity and heat capacity of a high-quality crystal CeAuSb2 with T_N of 6.8 K, the highest for this compound. The magnetic transition temperature is initially suppressed with pressure, but is intercepted by a new magnetic state above 2.1 GPa. The new phase shows a dome shape with pressure and coexists with another phase at pressures higher than 4.7 GPa. The electrical resistivity shows a T^2 Fermi liquids behavior in the complex magnetic state, and the residual resistivity and the T^2 resistivity coefficient increases with pressure, suggesting the possibility of a magnetic quantum critical point at a higher pressure.