Changes of exciton binding energies in InAlAs/InPBi/InAlAs quantum well with the well width, Al and Bi components are calculated using the variational method in the effective mass approximation. The effects of the applied electric field and magnetic field on exciton binding energy are analyzed. Results show that exciton binding energy increases firstly and then decreases with the increasing of well width. With the increasing of Al and Bi components, the exciton binding energy also increases gradually. Effect of the applied electric field which is smaller on the exciton binding energy is small. When the applied electric field is large enough, it will destroy the exciton effect. Exciton binding energy presents monotonous increasing tendency with the increasing of the applied magnetic field. The calculation results have certain guiding significance for applications of InAlAs/InPBi/InAlAs quantum well in optoelectronic devices.