For a specific GUI of my java web application, some members of my team have designed different web GUIs. Each of the designed GUIs has its own pros and cons. Is there a metric to evaluate a web GUI and score each designed one a “goodness mark”? I want to pick up that GUI that has the highest score. Or any tools is available for this evaluation?
Not really, because "goodness" means different things to different people. On a web site you might measure that as how many people make it to the checkout though different interface variations, or how quickly they find a page they're looking for or how long they stay on the site etc.
You could measure some things against known standards, accessibility for example and there are some very general design principles (a grid layout is generally better than random jumble for example, consistency in placement and ordering of buttons is another).
If your application has a sufficiently high number of users to make a sensible sample size then a typical approach is A/B testing where you serve different versions of the interface to different people and see what happens. However, you still need to decide on a goal to measure against (number of sales, time spent on site etc) to compare the two versions.
If you have a small user base or this is an internal application then direct user feedback might be the better option - i.e. just go and ask them which they find easier/better to use.