Without eval:
Your original string was not an actual string.
jsonObj = "{"TeamList" : [{"teamid" : "1","teamname" : "Barcelona"}]}"
The easiest way to to wrap it all with a single quote.
jsonObj = '"{"TeamList" : [{"teamid" : "1","teamname" : "Barcelona"}]}"'
Then you can combine two steps to parse it to JSON:
$.parseJSON(jsonObj.slice(1,-1))