Many critical electric grid operations rely on accurate grid frequency measurements. Unfortunately, the measurement accuracy can be easily undermined by power system transient faults. During a power system transient fault, the power grid voltages and currents are usually highly distorted by high-frequency components. What is worse, the power grid signals could have discontinuity during some system transient faults such as phase angle jump, and the discontinuity could result in large measurement errors to state-of-the-art grid measurement algorithms. In this study, a fault-tolerant grid frequency measurement algorithm during transients is proposed. The new algorithm consists of two stages. The first stage is a transient detector, and it can detect the occurrence of system transient faults instantaneously. The second stage is the intelligent frequency estimator, and it will adapt its measurements according to the transient detector. The performance of the algorithm is evaluated under different steady-state and transient conditions. Both dependability and security of the fault-tolerant algorithm are assessed by using PSCAD simulation data and IEEE Standard test data.