The　main　purpose　of　this　paper　is　to　solve　the　variational　problem　containing　real-　and　complex-order　fractional　derivatives.　We　define　a　new　version　of　the　complex-order　derivative　based　on　the　psi-Riemann-Liouville　fractional　derivative,　and　get　the　Euler-Lagrange　equation　for　the　variational　problem.　By　introducing　the　approximated　expansion　formula　of　the　complex-order　fractional　derivative　to　the　variational　problem,　we　derive　the　corresponding　approximated　Euler-Lagrange　equation.　It　is　proved　that　the　approximated　Euler-Lagrange　equation　converges　to　the　original　one　in　the　weak　sense.　At　the　same　time,　the　minimal　value　of　the　approximated　action　integral　tends　to　the　minimal　value　of　the　original　one.　We　also　conduct　a　stress　relaxation　experiment　and　discuss　the　feasibility　of　the　complex-order　derivative　in　real　problem　modeling.