Vibration measurement and analysis has been an accepted method since decades to meet a number of objectives - machinery condition monitoring, dynamic qualification of any designed structural components, prediction of faults and structural aging-related problems, and several other structural dynamics studies and diagnosis. However, the requirement of the vibration measurement at number of locations in structures, machines and/or equipments makes the vibration measurement exorbitant if conventional piezoelectric accelerometers are used. Hence, there is a need for cheaper and reliable alternative for the conventional accelerometers. The Micro-Electro-Mechanical Systems (MEMS) accelerometers are one such cheap alternative. However, a significant deviation in the performance of the MEMS accelerometers has been observed in earlier research studies and also confirmed by this presented study when compared with well known conventional accelerometer. Therefore, two methods have been suggested to improve the performance of the existing MEMS accelerometers; one for correction in time domain and other in frequency domain. Both methods are based on the generation of a characteristic function (CF) for the MEMS accelerometer using well known reference accelerometer in laboratory tests. The procedures of both methods have been discussed and validations of these methods have been presented through experimental examples. In addition, a Finite Element (FE) model of a typical MEMS accelerometer has been developed and modal analysis has been carried out to understand the dynamics of capacitive type MEMS accelerometer and to identify the source of errors. It has been observed that the moving fingers behave like a cantilever beam while the fixed fingers showed rigid body motion. This cantilever type of motion seems to be causing non-parallel plates effect in the formed capacitors between moving and fixed fingers which results in errors in the vibration measurement. Hence, design modifications on finger shape have been suggested to remove the cantilever motion and results showed remarkable improvement. Moreover, the effect of using synchronous amplitude modulation and demodulation in the readout circuit has been studied. The experimental study showed that this circuit also introduces errors in amplitude and phase of the output signal compared with the input signal. Thus, in the new design of MEMS accelerometers, improvements in both mechanical design and electronic circuit are required.