I'm trying to select edges with loop selection, But there is part of edges isolated which seemed to be made when I bevelled. But I want to them to be loop in order to bevel more. There is no separated vertices so I cannot merge them by using Remove doubles. How can I connect those three edges together?
The question you'd need to ask yourself is:
"How does Blender know where a loop is running along anyways?"
Basically, a loop can only be found if there is four edges connecting to a point. See this GIF for illustration:
I'm selecting the two edges first which are the loop that I intend to select, then the two perpendicular edges that branch off from them. Loop selection takes a single edge as an input (the one you click on), and follows the path along this direction UNTIL there is a case where a different amount than four edges are forming a vertex point. Along this path, the edge that is "in the middle" will be the one considered to form the loop. As your beveled edge gives you a corner case where only three edges meet, loop selection stops there. How would Blender know if you want to go left or right?
To do the selection you want, try either Shortest Path select by Ctrl + RMB clicking, like this:
or select the faces which are inside the desired loop, and use the boundary select tool from the menu like this: