Structural health monitoring (SHM) is important for the operational safety and stability of industrial pipeline systems. In this paper, a data-driven and finite-element-based method for pipe crack-grade identification and the explainable framework are developed. Specifically, an ultrasonic guided wave pipe crack grade identification model based on improved one-dimensional convolutional neural network is proposed, in which the multi-size convolutional kernels are used to replace the traditional single-size kernels. Thus, the developed method can effectively extract the crack information and achieve end-to-end identification. Moreover, a framework for crack-grade identification attribution analysis is developed by using the local interpretable model-agnostic explanations (LIME) theory, in which the marginal contribution values corresponding to different features can be obtained by calculating the LIME value. Finally, effectiveness of the developed methodology is comprehensively verified by simulation and physical experiments. Experimental result show that the developed methodology can obtain accurate and robust performance for pipe crack-grade identification under various noise conditions.