State-of-the-art process technology offers ultra-low power devices operating at ultra-low voltages. However, they show a considerable level of non-linear characteristics. Hence, the accuracy of cell delay and variation modeling for logic cells is expected to be very low with a linear interpolation. In this paper, we propose a compressive sensing based high non-linear cell delay and variation modeling. This paper introduces accuracy optimization methods to fit the delay and variation modeling by pre-processing. Pre-processing is a hybrid approach combining a linear interpolation and compressive sensing for accurate restoration with using less samples. With FinFET cell delay and variation modeling, the experimental results show that the proposed method can obtain a similar or better accuracy with a half of measurement samples than a conventional linear interpolation based modeling.