The effects of combustion on turbulent statistics in a supersonic turbulent jet are investigated by using direct numerical simulation (DNS). To study the combustion effects, two DNS cases (reacting case and non-reacting case) are conducted and the comparison of turbulent statistics are used to study the combustion effects. The medium of jet is $85\%$ hydrogen with temperature $305K$ and the co-flow is hot air with temperature $1150K$. The Reynolds numbers based on the jet diameters are $22000$ and the jet Mach numbers are $1.2$. The DNS results show that combustion case has both larger decay rate constant of centerline streamwise mean velocity and larger spreading rate of half-velocity jet width than the non-reacting case. It also shows that the combustion case achieves the self-similarity slower. For reacting jet, the vortex structures are more smooth in the near field and vortex filament structures are larger in the far field. Combustion causes the turbulent zone to be delayed downstream and increases the probability of strong velocity pulsation.