Accelerator driven subcritical system (ADS) is a kind of clean nuclear facility with inherent safety features. ADS facilities mainly put emphasis on studying the two following categories of isotopes, namely, the minor actinide (MA) and long-lived fission products (LLFP). However, some general burnup codes lack depletion chains for specific heavy isotopes with MA included, or treat a series of isotopes, including LLFP, as pseudo nuclides. Taking into account the above characteristics, a burnup-transport code system OMCB (OpenMC based Burnup code) has been developed based on transmutation trajectory analysis (TTA) method and Bateman equations, coupling with OpenMC code for ADS facilities. In order to make the depletion calculation process more effective and accurate, three kinds of iterations and one terminate criteria have been proposed for searching the depletion chains. Moreover, a scan mode method based high order differential expression has been proposed to remove the infinite terms in Bateman equations. Finally, a concept of sub-step predictor calculation has been introduced by combining both linear and quadratic interpolation methods, which makes cross section time-dependent in each depletion step. Four benchmarks have been used to validate OMCB code. The numerical tests demonstrate that OMCB code has a good agreement in comparison with the reference results and can be used in ADS facilities.