During the early developmental stages of solid rocket motors (SRMs), particularly under extreme operating conditions, the scarcity of experimental data severely limits the predictive capabilities of conventional deep learning models. To address this challenge, this paper proposes a novel hybrid predictive framework, termed Shape-Regularized Meta-Variational Multi-Scale Network (SR-MVSNet), tailored for few-shot thrust prediction via shape-regularized meta-learning. First, a variational autoencoder (VAE) maps nine static design and operating parameters to a latent probability distribution and reconstructs the parameter vector. A parallel multi-scale convolutional neural network (MSCNN) then processes the reconstructed features to predict the complete thrust curve. Crucially, a joint loss function with shape regularization is integrated within the model-agnostic meta-learning (MAML) architecture, guiding the network to reproduce the measured thrust build-up and decay through supervised first- and second-order difference matching. Experimental results demonstrate that the proposed framework achieves the lowest mean squared error among the evaluated models in the low-temperature-to-ambient-temperature transfer task. Notably, during the critical steady-state combustion phase, the mean absolute percentage error is 1.71% under the combined-source task, supporting accurate steady-state thrust prediction for the rapid performance evaluation of SRMs in engineering applications.