We present the study of the conductance of a quantum nanosystem containing afinite-sizeattractive impurity. A single finite-size attractive impurity introduces multiple quasi-bound states in the channel for a sufficiently strong attractive potential, and these states give rise to multiple resonant peaks before the first plateau in the conductance. These resonant peaks, arising from the resonant tunneling through the multiple quasi-bound levels, have a Lorentzian shape centered around the resonant energy and exhibit a dramatic variation in the linewidths with resonant energy. The strength of the attractive impurity in the constriction is shown to strongly affect the resonant energy and the mean lifetime of each tunneling peak. The temperature dependence of the resonant peaks of conductance is also discussed. ©1997 American Institute of Physics.