Time series forecasting (TSF) plays a crucial role in many real-world applications, such as weather prediction and economic planning. While Transformer-based models have shown strong capabilities in modeling long-range dependencies, effectively capturing the multi-scale temporal dynamics inherent in time series remains a major challenge. Existing methods often adopt time-windows of varying sizes, which may introduce noisy or irrelevant representations when mismatched with the underlying temporal patterns, potentially leading to overfitting. In this paper, we propose Sparse-Scale Transformer (SSformer) with Bidirectional Awareness for Time Series Forecasting to enhance the multi-scale modeling for time series. Specifically, we propose a novel Sparse-Scale Convolution (SSC) block that imposes sparsity on scales to obtain the informative representations by evaluating the intra-scale segment similarity of time series, and utilizes scale-specific convolutions to extract local patterns. Furthermore, we design a Bidirectional-Scale Interaction (BSI) block to explicitly model scale correlations in both coarse-to-fine and fine-to-coarse directions. Finally, scale predictions are ensembled to fully exploit the complementary forecasting capabilities across scales. Extensive experiments on various real-world datasets demonstrate that SSformer achieves state-of-the-art performance with superior efficiency. Code is available at \url{https://github.com/yingliu-coder/SSformer}.