I assume based on your profile that you're talking about The Ultimate Doom, since Doom 3: BFG shouldn't be having that issue. (Though you do mention "first episode", so that's also a clear tip off)
Are you playing Ultimate Doom through DOSBox? Or are you using a source port like GZDoom or similar? If it's just DOSBox, then you'll likely want to look for and edit the configuration file (ultimate.conf or ultimatem.conf, I think are the ones to look for). Look for this line (these will be without the " marks in your file): "fullscreen=" which will probably have something like "original" already set in it after the =. Just change "original" to "desktop" and save the file.
(edit) You may also want to change other settings in the configuration file(s) as needed. Particularly fulldouble= (if it's set to "true" then change it to "false") and aspect= (set it to "true" and it will maintain the correct aspect ratio while in fullscreen).
Alternately, using a source port like
GZDoom, you'll have less issues fighting with settings like this as they're built with more modern setups in mind. But you don't need to use a port if you're fine with DOSBox overall (certainly use and play what you prefer and what works best for you).