Terahertz (THz) radiation lies between the millimeter and infrared region of the electromagnetic spectrum, which is typically defined as the frequency range of 0.1–10 THz and the corresponding wavelength ranges from 30 μm to 3 mm. Terahertz radiation due to wide spectrum, high penetration, low energy, and other important features, has been a valuable tool for imaging and non-destructive testing on a submillimeter scale. Continuous-wave (CW) terahertz ptychography is a type of phase-contrast technique with advantages of simple set-up and large field-of-view. It retrieves the complex-valued transmission function of the specimen and the probe function at the same time. The extended ptychographic iterative engine (ePIE) algorithm is used as the reconstruction algorithm in the field of ptychography, because it is relatively simple, and can use computer memory efficiently. However, the problem of algorithm convergence delay makes us unable to acquire the reconstruction result very quickly. Since the ptychography is a problem of retrieving phase information, physical constraints affect the convergence speed of the algorithm strongly. In this paper, we propose a dual-plane ePIE (dp-ePIE) algorithm for CW THz ptychography. By moving detector along the axis and capturing diffraction patterns of one zone of an object at two recording planes, then, two sets of patterns used as the constraints simultaneously can increase the diversity of experimental parameter. Hence, the convergence rate can be improved. The simulation results suggest better reconstruction fidelity with a faster convergence rate by the dp-ePIE algorithm. The dual-plane terahertz ptychography experimental setup is built based on 2.52 THz optically pumped laser and Pyrocam-III pyroelectric array detector. Compared with other methods to increase the diversity of measurement, the setup of dual-plane ptychography can be compact and simple, thus reducing the terahertz wave transmission loss. A polypropylene sample is adopted and it is approximated as a pure phase object. No-reference structural sharpness (NRSS) is utilized as a quantitative evaluation index. It takes 45.086 s to achieve NRSS value of 0.9831 by using the dp-ePIE algorithm in 10 iterations, while the NRSS value and calculation time for e-PIE algorithm are 0.9531 and 57.117 s (20 loops), respectively. The experimental results show that the dp-ePIE algorithm can obtain high-quality amplitude and phase distribution with less iterations than the traditional ePIE algorithm.