In-line digital holography usually employs a phase retrieval algorithm to decouple the phase information but fails to eliminate the unwanted DC and twin image terms when the measured sample does not agree with the sparsity. While the off-axis digital holography can efficiently remove the unwanted image terms but can not reserve the high frequencies of the sample to realize high resolution. The in-line-and-off-axis hybrid digital holography was then developed to provide a relatively high resolution digital holographic imaging without considering the effect of the unwanted terms. In other words, the in-line-and-off-axis hybrid digital holography merges all of the best virtues of the mentioned-above methods in an efficient and elegant way. However, this state-of-the-art method requires prior knowledge about the diffraction distance, which results in time-consuming and low accuracy. In other sense, telecentric technology can realize non-diffractive imaging without the knowledge about the diffraction distance or spherical aberration or defocusing aberration. Therefore, in this paper, a novel in-line-and-off-axis hybrid digital holography is proposed by introducing telecentric imaging architecture, and the corresponding reconstruction method is further proposed by utilizing constrained iterative approach. In this method, telecentric in-line-and-off-axis hybrid digital holography is first used to acquire focused off-axis and in-line holograms, respectively. The low resolution phase information is reconstructed from the off-axis hologram by using Fourier transform method with the help of the sample-free off-axis hologram, and then multiplexed with the amplitude information obtained from the in-line hologram to act as the initial complex amplitude in the iterative recovery process. As a result, constrained iterations are carried out in the spatial domain and frequency domain to realize high resolution and high speed reconstruction. After simulations, we build an experimental setup and demonstrate the operation of the method with USAF resolution target, onion cells and bee wings. Both the simulation and experimental results show that the proposed method can require no prior knowledge to suppress the phase disturbance caused by the unwanted image terms and optical aberrations, resulting in high speed and full utilization of spatial bandwidth product of the digital camera to yield high resolution reconstruction. We hope that the proposed method will have most practical applications in the case where large resolution, high speed and good quality are needed.