You are trying to Insert a new record, For updating an existing record you need to use UPDATE
command see below.
CREATE PROCEDURE [dbo].[ChangePassword]
@User_ID varchar(30),
@Password varchar(20)
AS
BEGIN
SET NOCOUNT ON;
UPDATE [User]
SET [Password] = @Password
WHERE [USER_ID] = @User_ID
END
Also avoid using sql-server key words as your column names, if you do have some columns like that make sure you use square brackets []
around them when using inside a query.