In this paper，the bi-levl programming model is proposed to study the continuous network design problem with the second-best credits charging under elastic demand． The upper level decision maker maximizes the total social benefits by choosing the link enhancement and link credit charging． The lower level decision makers ( the users) choose their optimal paths to minimize their generalized travel costs including the travel time and the value of credit for using the credit-charging link． By replacing the lower level programming problem with its Karush-Kuhn-Tucker( KKT) conditions，the bi-level programming model can be transformed into a single level problem． To deal with the difficult slackness conditions in the above single level problem，we propose a relaxation algorithm to solve it． Numerical experiments demonstrate the feasibility of the proposed model and algorithm． The numerical results show that this proposed model can obtain better effects to alleviate the congestion． It will be convenient and feasible to implement if we improve the link enhancement and charge the credit only in the subset of the network． In this proposed model，the users who travel more should buy the credits from the market and pay money for those additional travel need． While the users who reduce their travel can sell their extra credits to compensate their inconvenience for reducing travel． Thus，this tradable credit scheme is revenue neutral．