A　novel　numerical　time-domain　method,　referred　to　as　Maxwell-Minkowski　precise　integration　time-domain　(MM-PITD)　method　which　combines　MM　equations　and　the　precise　integration　(PI)　technique,　is　developed　in　this　paper　to　solve　the　problems　involving　moving　objects.　In　the　proposed　method,　the　computation　cells　in　different　regions　bear　different　governing　equations　for　electromagnetic　fields.　With　the　suggested　criterion　to　distinguish　the　governing　equations　in　these　cells,　the　discretized　formulations　for　the　whole　computation　domain　are　obtainable.　Since　the　coefficient　matrix　used　in　the　PI　technique　is　required　to　be　constant　or　piecewise　constant,　an　approximation　approach　to　locally　linearizing　the　time-variant　equation　system　is　provided.　Two　appealing　superiorities　of　the　proposed　method　to　other　methods　are:　1)　the　speed　of　the　object　can　be　either　constant　or　time　variant　and　2)　multiple　objects　can　be　taken　into　account　conveniently.　In　addition,　the　proposed　method　is　more　efficient　compared　with　the　other　methods　wherein　two　or　more　coordinate　frames　are　used.　Several　numerical　experiments　are　carried　out　to　test　the　MM-PITD　method.　Its　effectiveness,　efficiency,　and　generality　are　thereby　confirmed.