How to keep leading zeros in csv file when working with QGIS

I'm new to QGIS, and Geographic Information Systems in general, and also have no experience with informatics.

I a have shapefile which works fine, and then I have a file in CSV format, and I try to join these two files, using a column which should be equal between two files. The problem is, some of the numbers have leading zeros (they are some sort of postcode in my country), that disappear from the CSV file when I import it to QGIS...

Is there any simple way to keep leading zeros?

In the shapefile the leading zeros don't disappear.