It sounds like you are importing with the "Copy" option selected, and not the "Add" option.
Either that, or you have selected to make a 2nd copy on Import (this option is on the right under File Handling in the Import dialog box)
It depends on your exact import process: it's likely that LR is merely doing what it is told, but that is the opposite to what you think is happening.
If you copy them onto your HD yourself, and then import them via LR, then ensure you have "Add" selected and not "Copy".
If that isn't the case, make that "Make a second copy isn't selected".