In order to explain the phenomenon of negative capacitance (NC) in light emitting diodes LEDs, we present a new model based on local strong recombination in active region and firstly deduce the analytic expression of NC from continuity equation. The theoretical result indicates that the NC effeci becomes stronger when the carrier recombination rate increases in a certain range, which is consistent with the experimental result. Accordingly, we confirm that the NC is caused by carrier recombination in active region instead of by other exterior factors. This work was supported by the National Nature Science Foundation (Grant No. DMR-60376027).