Dual Energy CT (DECT) has recently gained significant research interest owing to its ability to discriminate materials, and hence is widely applied in the field of nuclear safety and security inspection. With the current technological developments, DECT can be typically realized by using two sets of detectors, one for detecting lower energy X-rays and another for detecting higher energy X-rays. This makes the imaging system expensive, limiting its practical implementation. In 2009, our group performed a preliminary study on a new low-cost system design, using only a complete data set for lower energy level and a sparse data set for the higher energy level. This could significantly reduce the cost of the system, as it contained much smaller number of detector elements. Reconstruction method is the key point of this system. In the present study, we further validated this system and proposed a robust method, involving three main steps: (1) estimation of the missing data iteratively with TV constraints; (2) use the reconstruction from the complete lower energy CT data set to form an initial estimation of the projection data for higher energy level; (3) use ordered views to accelerate the computation. Numerical simulations with different number of detector elements have also been examined. The results obtained in this study demonstrate that 1 + 14% CT data is sufficient enough to provide a rather good reconstruction of both the effective atomic number and electron density distributions of the scanned object, instead of 2 sets CT data.