A　non-singular　terminal-sliding-mode　(NTSM)　observer　which　contains　a　high-order　sliding　mode　is　introduced　into　a　direct　torque　control　(DTC)　system　of　permanent　magnet　synchronous　motor　(PMSM).　The　proposed　system　uses　the　non-singular　terminal-sliding-mode　observer　to　obtain　the　back　electromotive　force　which　is　used　to　estimate　the　rotor　position　and　speed　of　PMSM　for　sensorless　DTC　system.　Compared　with　the　conventional　sliding　mode　observer,　NTSM　observer　without　the　low-pass　filter　can　avoid　the　problem　of　speed　estimation　lag　and　phase　lag,　and　contains　the　integral　element,　decreases　ripple,　reduces　static　errors.　The　numerous　simulation　results　proved　that　the　proposed　algorithm　improves　the　speed　estimation　precision　and　dynamic　performance　of　system.