Although multi-scale feature learning can improve the performances of deep models, its parallel structure quadratically increases the model parameters and causes deep models to become larger and larger when enlarging the receptive fields (RFs). This leads to deep models easily suffering from over-fitting issue in many practical applications where the available training samples are always insufficient or limited. In addition, under this limited situation, although lightweight models (with fewer model parameters) can effectively reduce over-fitting, they may suffer from under-fitting because of insufficient training data for effective feature learning. In this work, a lightweight model called Sequential Multi-scale Feature Learning Network (SMF-Net) is proposed to alleviate these two issues simultaneously using a novel sequential structure of multi-scale feature learning. Compared to both deep and lightweight models, the proposed sequential structure in SMF-Net can easily extract features with larger RFs for multi-scale feature learning only with a few and linearly increased model parameters. The experimental results on both classification and segmentation tasks demonstrate that our SMF-Net only has 1.25M model parameters (5.3% of Res2Net50) with 0.7G FLOPS (14.6% of Res2Net50) for classification and 1.54M parameters (8.9% of UNet) with 3.35G FLOPs (10.9% of UNet) for segmentation but achieves higher accuracy than SOTA deep models and lightweight models, even when the training data is very limited available.