<p>Crying is the primary way infants communicate and presents a significant challenge for new parents to understand the underlying reasons. The classification of infant cries is challenging due to redundant and inappropriate signal features in data that lead to lower classification accuracy. This research proposes Inertia Weight-Path Finder Algorithm (IW-PFA) based feature selection method to choose appropriate features from the whole feature subsets based on the feature importance to enhance infant cry classification performance. Then, the stacked Gated Recurrent Unit with self-attention (stacked GRU with self-attention) based classifier is used to classify the different classes of infants with high accuracy. The stacked GRU captures hierarchical patterns in data by incorporating self-attention mechanism that minimizes the gradient vanishing issue, offering a better classification performance. The proposed method is evaluated using two infant cry datasets, Baby Chillanto (BC) and Donate Cry Corpus (DCC) datasets. The proposed IW-PFA and stacked GRU with self-attention method attained a high accuracy of 99.73% on BC, while 96.69% on DCC datasets. The proposed method performs well in terms of accuracy when compared to the conventional techniques, Optimized Granule Based Fuzzy Rules (OGBFR) and Sparse Autoencoder Long Short-Term Memory based Generative Adversarial Network (SLGAN).</p>