This study proposes a neural network–based acceleration framework to enhance the computational efficiency of topology optimization using the Solid Isotropic Material with Penalization (SIMP) method. In conventional SIMP-based optimization, finite element analysis on dense meshes is repeatedly performed, leading to significant computational cost. To address this limitation, convolutional neural networks (CNNs) are employed to exploit the spatial correlations among structural elements and learn the evolution patterns of density fields from nonlinear optimization histories. Specifically, the proposed approach predicts near-optimal density distributions by mapping density fields from early iterations to those close to convergence, thereby reducing the number of required SIMP iterations. The proposed method captures element evolutionary trends regardless of optimization conditions, allowing the trained model to generalize across diverse boundary conditions. Moreover, the abundant evolution data derived from the optimization process significantly decreases the cost of data acquisition. More importantly, incorporating the spatial correlation of element evolution can effectively avoid the occurrence of defective structures compared to element itself. Furthermore, a novel training strategy is introduced that inputting density evolution in the later stage of optimization can enhance binary characteristic of predicted structures, which effectively reduces the size of the training dataset. The performance of the proposed CNN-accelerated SIMP framework is investigated through several benchmark topology optimization problems in both 2D and 3D. The advantages of incorporating spatial correlations are validated through challenging examples involving corner contacts and disconnected structural components. In addition, numerical experiments demonstrate that the framework reduces optimization iterations by 82.96% for 2D and over 75% for 3D problems without compromising structural performance, even when applied to unseen geometries, boundary conditions and non-design domains.