Minecraft: Replaces blocks?

This only happens on occasion but sometimes when I play Minecraft on singleplayer, not open to lan, the blocks I try to mine would blink when I break them and reappear. Then a few seconds later, the block would fall and I can obtain it. It doesn't seem to be lagging because when I walk around and do other things, it works fine, it's only when I try to mine blocks. Like I said, it only happens on occasion, but it's pretty annoying, is there anything I can do to fix it?