Training Large Language Models (LLMs) from scratch requires immense computational resources, making it prohibitively expensive. Model scaling-up offers a promising solution by leveraging the parameters of smaller models to create larger ones. However, existing depth scaling-up methods rely on empirical heuristic rules for layer duplication, which result in poorer initialization and slower convergence during continual pre-training. We propose \textbf{LESA}, a novel learnable method for depth scaling-up. By concatenating parameters from each layer and applying Singular Value Decomposition, we uncover latent patterns between layers, suggesting that inter-layer parameters can be learned. LESA uses a neural network to predict the parameters inserted between adjacent layers, enabling better initialization and faster training. Experiments show that LESA outperforms existing baselines, achieving superior performance with less than half the computational cost during continual pre-training. Extensive analyses demonstrate its effectiveness across different model sizes and tasks.