Due to the huge data storage and transmission pressure, sparse data collection strategy has provided opportunities and challenges for 3-D SAR imaging. However, sparse data brought by the sparse linear array will produce high-level side-lobes, as well as the aliasing and the false-alarm targets. Simultaneously, the vectorizing or matrixing of 3-D data makes high computational complexity and huge memory usage, which is not practicable in real applications. To deal with these problems, tensor completion (TC), as a convex optimization problem, is used to solve the 3-D sparse imaging problem efficiently. Unfortunately, the traditional TC methods are invalid to the incomplete tensor data with missing slices brought by sparse linear arrays. In this paper, a novel 3-D imaging algorithm using TC in embedded space is proposed to produce 3-D images with efficient side-lobes suppression. With the help of sparsity and low-rank property hidden in the 3-D radar signal, the incomplete tensor data is taken as the input and converted into a higher order incomplete Hankel tensor by multiway delay embedding transform (MDT). Then, the Tucker decomposition with incremental rank has been applied for completion. Subsequently, any traditional 3-D imaging methods can be employed to obtain excellent imaging performance for the completed tensor. The proposed method achieves high resolution and low-level sidelobes compared with the traditional TC-based methods. It is verified by several numerical simulations and multiple comparative studies on real data. Results clearly demonstrate that the proposed method can generate 3-D images with small reconstruction error even when the sparse sampling rate or signal to noise ratio is low, which confirms the validity and advantage of the proposed method.