According to reconstruction principle,a novel chaotic mapping was investigated,aiming at seeking for spreading sequences with excellent performance. The maximum Lyapunov exponent of the new chaotic mapping was increased from 0.697 to more than 5.5. The phase-space of the mapping has a weak and axially symmetric structure,and it was used to generate spreading sequences. Calculation and analysis show that the complexity,balance and correlation of those spreading sequences are all improved. On the basis of these results,it can be concluded that sequences produced by this new chaotic mapping are spreading sequences with outstanding performance.