We propose a theoretical model for predicting the impulse bit of bipropellant thrusters under pulse-firing operations. The present theoretical model, which considers the nonuniformity of the mixture ratios created inside the thrust chamber, extends the stream-tube approach, which is limited to the prediction of the steady performance. In pulse-firing operation, the fuel or the oxidizer alone can be injected in isolation due to the mismatched injection timing before the rated injection, which leads to the deterioration of performance as compared with the steady operation. The present approach (the unsteady stream-tube model) successfully implements a time-dependent stream-tube structure inside the thrust chamber, allowing for the prediction of the impulse bit as a straightforward function of the injection conditions. Three different pulse-firing tests using distinct hypergolic propellants demonstrate the validity of this model, typically reproducing the notable trend of deterioration in the impulse bit in the short-pulsed mode. We also examine the time-averaged specific impulse and mass flow rate to improve the impulse bit during short-pulsed operations.