During the measurement and transmission in power systems, the noise will interfere the data to varying degrees, and the accuracy of transient stability assessment (TSA) may be affected. With current methods, noisy data are usually denoised according to expected noise. However, the real noise distribution is complex. The data may be disturbed by noise such as mechanical characteristics of the prime motor, load fluctuation and signal interference during transmission. Noises from different sources have different characteristics. If the noise of the actual input data is different from the noise considered in the training, the output results of the denoising method for a certain noise are often unsatisfactory. Therefore, an adaptive data recovery model (ADRM) is proposed in this paper. ADRM can adaptively recover noisy data to low-noise data regardless of noise distribution, thus reducing the impact of noise on TSA. Firstly, a targeted data recovery model (TRM) based on stacked denoising auto-encoder is proposed, by which the noisy data with specific noise distribution can be recovered. Then, the ADRM composed of several TRMs and a noise recognition model (NRM) is constructed. The NRM is based on multi-layer perceptron, which can identify the noise distribution of the input data and assign weights to the data recovered by TRMs to obtain the combined recovered data. When the actual noise is similar to the noise trained for the TRM, the assigned weight is large for this model accordingly. Then, the recovered data are applied for TSA through the classification model. The effectiveness of this method is verified in IEEE 39-bus system and a realistic system.