In this report, a general analysis for optimal sensitivity of microbolometers with constant-current operation is described. Using a linear approximation of bolometer resistance with respect to temperature variation, close-form solution of the optimal condition can be obtained among a set of operational variables and device parameters, including the sensor resistance, TCR, thermal conductance and bias current or voltage. The solution is close to that calculated by the exact numerical method. It is found that, under constant-current operation, a stable (relative) maximum of the sensor responsivity can only be obtained for NTCR, bolometers. The maximum sensitivity may reach 106 V/W with practical parameters considered for uncooled FPA bolometers working in vacuum. At such conditions, a thermal detector may perform a D* value close to the BLIP condition, if it has a radiation-loss-limited feature. Also, a large-area single bolometer operated in the atmosphere may have a performance comparable to that of the present commercial pyroelectric detectors.