A function diagnostic system for use with an internal combustion engine having a filter provided in an exhaust passage of the internal combustion engine and an aqueous urea addition device located upstream of the filter in the exhaust passage, the filter supporting a selective reduction NOx catalyst that reduces NOx in exhaust gas using ammonia as a reducing agent and being configured to trap PM contained in the exhaust gas, and the aqueous urea addition device being configured to inject aqueous urea into the exhaust gas, the function diagnostic system comprising: a PM sensor to be provided downstream of the filter in the exhaust passage, the PM sensor having a pair of electrodes, the PM sensor being configured to output a signal corresponding to a deposition amount of the PM when the PM is deposited between the pair of electrodes and the pair of electrodes are electrically connected; and an electronic control unit configured to: calculate a NOx conversion rate in the filter; determine whether a NOx converting function of the filter is normal, based on the NOx conversion rate; execute a sensor regeneration process for removing the PM deposited between the electrodes of the PM sensor; continuously monitor an output value of the PM sensor after a predetermined PM deposition restart time, after execution of the sensor regeneration process is finished, the PM deposition restart time being a point in time at which deposition of the PM between the electrodes of the PM sensor is considered to be restarted; and determine that there is an abnormality in a PM trapping function of the filter, when the output value of the PM sensor, which has been continuously monitored, is reduced when the electronic control unit determines that the NOx converting function of the filter is in a normal status. a PM sensor to be provided downstream of the filter in the exhaust passage, the PM sensor having a pair of electrodes, the PM sensor being configured to output a signal corresponding to a deposition amount of the PM when the PM is deposited between the pair of electrodes and the pair of electrodes are electrically connected; and an electronic control unit configured to: calculate a NOx conversion rate in the filter; determine whether a NOx converting function of the filter is normal, based on the NOx conversion rate; execute a sensor regeneration process for removing the PM deposited between the electrodes of the PM sensor; continuously monitor an output value of the PM sensor after a predetermined PM deposition restart time, after execution of the sensor regeneration process is finished, the PM deposition restart time being a point in time at which deposition of the PM between the electrodes of the PM sensor is considered to be restarted; and determine that there is an abnormality in a PM trapping function of the filter, when the output value of the PM sensor, which has been continuously monitored, is reduced when the electronic control unit determines that the NOx converting function of the filter is in a normal status. calculate a NOx conversion rate in the filter; determine whether a NOx converting function of the filter is normal, based on the NOx conversion rate; execute a sensor regeneration process for removing the PM deposited between the electrodes of the PM sensor; continuously monitor an output value of the PM sensor after a predetermined PM deposition restart time, after execution of the sensor regeneration process is finished, the PM deposition restart time being a point in time at which deposition of the PM between the electrodes of the PM sensor is considered to be restarted; and determine that there is an abnormality in a PM trapping function of the filter, when the output value of the PM sensor, which has been continuously monitored, is reduced when the electronic control unit determines that the NOx converting function of the filter is in a normal status.