An effective strategy is proposed to solve the dilemma of second resource conflicts in the critical chain method ( CCM) from a novel perspective of robust optimization． Firstly，this dilemma is mathematically expressed to gain a quantitative model，and the logic of the dilemma resulted from insertions of feeding buffers is explored． Then scenario analysis is adopted and four basic components are decomposed from the complex conflict phenomena． Secondly，based on robust scheduling optimization，some effective policies are investiga-ted and classified for all sub-problems of conflict situations，and a local rescheduling strategy is developed．Moreover，a robust index is designed based on the strategy，which combines the two scheduling progresses with dynamic consumptions of two kinds of buffers． The optimal schedule is an output when maximizing the ro-bust index． Extensive numerical experiments and three performance indicators are constructed，which include the realized probability that a project finishes on schedule，the sum of the absolute deviations between the ac-tual and the planned activity starting times and the variance of the absolute deviations for activity starting times． Extensive numerical experiments are also performed on the set of instances randomly generated by Pro-gen． The experimental results show the values of three statistical indicators under the schedule of the robust CCM are better than those under the schedule of the traditional CCM． Finally，the conclusions indicate that the strategy to deal with the second resource conflicts and the robust measure exhibits good stable effects during project implementation．