Generalizing (non-commutative) Donaldson-Thomas invariants, I introduce counting invariants of complexes of coherent sheaves on a local Calabi-Yau 3-fold with fixed asymptotic behaviors, which depends on the choice of the t-structure. For some toric Calabi-Yau 3-folds, I provide a wall-crossing formula which does not depend on the choice of the asymptotic behavior. As a by-product, we get normalized generating functions which do not depend on the choice of the t-structure.