We study the sign inversion behavior of organic magnetoresistance (OMR) in organic thin-film devices, to elucidate the mechanisms governing the well-known OMR phenomenon. From the combination of a percolation theory with a magnetic field modulated bipolaron mechanism, we derive a model that accounts for OMR sign inversion (OMRSI) behavior. It exhibits how an applied magnetic field acts together with other factors (temperature, bias, and film thickness) on the device current. Under the framework of space-charge-limited current, we reproduce two kinds of OMRSI behavior. In the end, we discuss the influence of hyperfine field on OMRSI lines.