I've a chord progression G, A, Bm, A, repeating itself throuh whole song in a key of B minor....i mean How it will affect the listener and how they feel ..
The "feel" of the ending not only depends on your last chord, but the way you approach it (the chord progression immediately before the end). If you want to finish your piece on a stable chord without using the tonic, a common progression is using the II chord before finishing on the dominant V. One of many combinations. Without a stable ending cadence, you're probably going to get some kind of vague or suspenseful feel. Which may or may not be what you're going for. Best of luck!
The circular nature of most pop progressions start on the tonic and end the progression somewhere else so the progression may end somewhere else wanting to go back to the first chord. There are many, many examples of this and one I know of the top of my head is When I Come Around by Green Day.
The verse progression G D Em C and the last chord played is C, but it desperately wants to resolve back to a G and most covers I've seen of this song do eventually resolve back to the G after fanfare for that reason.
Now it's possible that you are perceiving B as the tonic, but based on the given information and having you always go back to G, I would bet G would sound more like the final resting place than Bm.