Understanding of electronic and optical features of single-walled carbon nanotubes (SWNTs) has been a central issue in science and nanotechnology of carbon nanotubes. We describe the detection of both the positive trion (positively charged exciton) and negative trion (negatively charged exciton) as a three-particle bound state in the SWNTs at room temperature by an in situ photoluminescence spectroelectrochemistry method for an isolated SWNT film cast on an ITO electrode. The electrochemical hole and electron dopings enable us to detect such trions on the SWNTs. The large energy difference between the singlet bright exciton and the negative and positive trions showing a tube diameter dependence is determined by both the exchange splitting energy and the trion binding energy. In contrast to conventional compound semiconductors, on the SWNTs, the negative trion has almost the same binding energy to the positive trion, which is attributed to nearly identical effective masses of the holes and electrons.