In an industrial batch, it is common to produce products with different grades, so only a limited number of data are available for each grade of product. The data are also easily contaminated by external disturbances and noise. The sampling interval would be messy and irregular if contaminated samples were removed. Thus, it is difficult to build models for monitoring the corresponding process. This paper proposes a meta-learning-based functional continuous state space model for fast modeling and monitoring of multi-grade batch processes. It takes advantage of wavelet function properties to effectively handle the irregular sampling issue. In addition, the meta-learning method uses diverse historical multi-grade datasets for modeling. It rapidly establishes an efficient and reliable monitoring model for new running batches with a small number of batch data. The effectiveness of the proposed method is shown through a numerical case and an industrial case in the chemical batch process.