Strap-down air borne gravimeter is the core sensor of strap-down gravimetry system. In this paper, A new strap-down airborne gravimeter called SGA-WZ has been developed by the Laboratory of Inertial Technology of the National University of Defense Technology. Precise gravity anomaly data reconstruction is the key technology in airborne gravimetry based on the SGA-WZ. This paper explores a method for large scale precise gravity anomaly data reconstruction using the theory of Compressed Sensing (CS). Based on the CS theory, the gravity anomaly data reconstruction can be transformed into the one-norm convex quadratic program to be solved by several methods such as interior point methods (IPM). This paper presents an improved IPM for performing the large scale gravity anomaly data reconstruction precisely that uses the Preconditioned Conjugate Gradients Algorithm (PCG) to compute the search direction. And then, a flight test has been carried out in China with SGA-WZ. The test results have shown that the PCG-IPM algorithm can reconstruct the large scale gravity anomaly data with higher accuracy than the existing nearest interpolation method in airborne gravimetry. Read more..