The problem has resolved after updating the project to Spring'16. Actually when I created the project that time Force.com IDE plugin version is 32.0... and I was able to open the class in Salesforce Web. After updating the Force.com IDE version to 36.0..., I noticed one pop up every time when I open the eclipse informing that Project [Project name] was created with a previous version of Force.com IDE and needs to be updated to Spring'16. Begin the upgrade wizards now? Every time I clicked on No button and trying to open the class in Salesforce Web but didn't succeed. But once I update the project then Show in Salesforce Web feature start working again.
I don't know that what happen when updating the project to Spring'16, but it solves the problem. Hope it helps others also who were fighting with this situation.
If anyone could know the better solution then please share with me.