We report a highly sensitive wide-range resonant pressure sensor. The concept is based on tracking multiple modes of vibration of an electrothermally heated initially curved micro-beam experiencing the veering phenomenon between its first and third vibration modes. For low values of pressure, the third resonance frequency is very sensitive, and thus its variation with pressure is monitored and recorded. As increasing pressure, the resonance frequency of the third mode decreases until reaching the veering phenomenon. At that point, the first mode exchanges role with the third mode, becoming very sensitive, and hence its frequency is tracked afterward as varying pressure. We show that using this concept, the sensitivity of the resonant pressure micro-sensor is significantly enhanced. Finite element method (FEM) simulations and experimental data show that the proposed micro-sensor becomes highly sensitive for wide-range of pressure from 38 mTorr to 200 Torr. The effect of various parameters on the performance of the proposed pressure sensor is investigated including the thickness of the micro-beam, the vacuum chamber size, and the thermal actuation load.