Hi Joyanta,
I'm not sure that is supported out of the box in Kentico, but with simple code changes, you can modify it easily. You should take a look into SetupControl method in cms.calendar.ascx.cs. You can find it on this path: CMSWebParts/Viewers/Documents/cmscalendar.ascx. There is a line of code where is as default value assigned current date:
calItems.TodaysDate = TimeZoneMethods.ConvertDateTime(DateTime.Now, this);
You should change that to something like this:
var month = ValidationHelper.GetInteger(QueryHelper.GetString("month", ""), DateTime.Now.Month);
var date = new DateTime(DateTime.Now.Year, month, 1);
calItems.TodaysDate = TimeZoneMethods.ConvertDateTime(date, this);
This will select month passed from url in current year. Url should look like /some-page-name?month=1
You can use this to convert month name to int (check this post), but handle it properly for correct values:
int month = DateTime.ParseExact("January", "MMMM", CultureInfo.CurrentCulture ).Month
NOTE: It's not desirable to make changes on kentico's files, because next upgrade could replace your changes. You should clone 'Calendar' web part and make changes on custom file.
Best regards,
Dragoljub