Abstract: A spatial direct numerical simulation (DNS) was performedto study the turbulent statistical characteristics in the turbulent boundarylayer on a blunt cone with an adiabatic wall at an oncoming Mach 2.5, zeroangle of attack and the cone semi-angle of 5^\circ in this paper. Theresults were compared with the simulated cases of the supersonic turbulent boundarylayer over a flat plate and the hypersonic turbulent boundary layer on ablunt cone at Mach 6, suggesting the influence of the turbulent statisticswith the cone effect. The results showed that, the cone effect issignificant on the mean temperature profile and the compressibility, butunimportant on the scaling velocity law, the distribution of Reynolds stressand the budget of turbulent kinetic energy.