I have a Map Image that I got from OpenstreetMap(Osmarender Image ) .My question is

how to convert geographic coordinates to the co-ordinates of my picture (that is in pixels on X and Y on a picture). That is I receive geographic coordinates and it is necessary for me to draw this point on my picture.

Is there any API availabel in QT for processing this type of Map Problem

I'm not sure how you'd do a direct conversion, but I'm assuming you're using their REST API. There's probably a call you can make to the server that when given the location, it'll send back the lat/long coordinates.