We developed CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) with a perpendicularly magnetized synthetic antiferromagnetic (p-SAF) reference layer for magnetic sensor applications. The MTJs exhibited linear tunnel magnetoresistance curves to out-of-plane applied magnetic fields with dynamic ranges more than ±2.5 kOe, which are wider than those in CoFeB/MgO/CoFeB-MTJs reported to date. The performance metrics of MTJ sensors, i.e., sensitivity and nonlinearity, depend significantly on the anisotropy field of the free layer. We explained the dependences by a simple model based on the Stoner-Wohlfarth and Slonczewski models, which gives us a guideline to design the sensor performance metrics. These findings demonstrated that MTJs with a p-SAF reference layer are promising candidates for wide-dynamic-range magnetic sensors.