This is the case if the sample rates differ. make sure the audio file is the same sample rate as your Logic project.
You can either change your Logic project to the same sample rate as the voice over, or open the Media area, and go to the Bin Tab.
Select the voice over audio file. Right click on it and choose Copy/Convert File
Save this as a new file, and under File Conversion Settings choose the same sample rate as the Logic project. It will now convert the file to the new sample rate.