The Trefftz method is a truly meshless boundary-type method,because the trial solutions automatically satisfy the governing equation.In order to stably solve the backward wave problem and the inverse source problem,which both known to be highly ill-posed,we develop a multiple-scale polynomial Trefftz method(MSPTM),of which the scales are determined a priori by the collocation points.The MSPTM can retrieve the missing initial data and unknown source very well.As a by-product the present method can solve the wave propagation equation long term.Several numerical examples demonstrate that the present method is efficient and stable,even for those of strongly ill-posed ones under large noises.