Recent years have witnessed the prevalence of memory-based methods for Semi-supervised Video Object Segmentation (SVOS) which utilise past frames efficiently for label propagation. When conducting feature matching, fine-grained multi-scale feature matching has typically been performed using all query points, which inevitably results in redundant computations and thus makes the fusion of multi-scale results ineffective. In this paper, we develop a new Point-based Memory Network, termed as PMNet, to perform fine-grained feature matching on hard samples only, assuming that easy samples can already obtain satisfactory matching results without the need for complicated multi-scale feature matching. Our approach first generates an uncertainty map from the initial decoding outputs. Next, the fine-grained features at uncertain locations are sampled to match the memory features on the same scale. Finally, the matching results are further decoded to provide a refined output. The pointbased scheme works with the coarsest feature matching in a complementary and efficient manner. Furthermore, we propose an approach to adaptively perform global or regional matching based on the motion history of memory points, making our method more robust against ambiguous backgrounds. Experimental results on several benchmark datasets demonstrate the superiority of our proposed method over state-of-the-art methods.