In this Letter, we demonstrate a highly sensitive multi-stage terahertz (THz) wave parametric upconversion detector based on a KTiOPO4 (KTP) crystal pumped by a 1064-nm pulsed-laser (10 ns, 10 Hz). The THz wave was upconverted to near-infrared light in a trapezoidal KTP crystal based on stimulated polariton scattering. The upconversion signal was amplified in two KTP crystals based on non-collinear and collinear phase matching, respectively, to improve detection sensitivity. A rapid-response detection in the THz frequency ranges of 4.26-4.50 THz and 4.80-4.92 THz was achieved. Moreover, a dual-color THz wave generated from THz parametric oscillator using KTP crystal was detected simultaneously based on dual-wavelength upconversion. The minimum detectable energy of 2.35 fJ was realized with a dynamic range of 84 dB at 4.85 THz, which gives a noise equivalent power (NEP) of the order of 21.3 pW/Hz1/2. By changing the phase-matching angle or the wavelength of the pump laser, it is suggested that the detection of the THz frequency band of interest in a wide range from approximately 1 to 14 THz is possible.