Autonomous Underwater Vehicle (AUV) can be utilized to directly measure the geomagnetic map in deep sea. The traditional map interpolation algorithms based on sampling continuation above the sea level yield low resolution and accuracy, which restricts the applications such as the deep sea geomagnetic positioning, navigation, searching and surveillance, etc. In this letter, we propose a Three-Dimensional (3D) Compressive Sensing (CS) algorithm in terms of the real trajectory of AUV which can be optimized with the required accuracy. The geomagnetic map recovered with the CS algorithm shows high precision compared with traditional interpolation schemes, by which the magnetic positioning accuracy can be greatly improved.