The crescent nanostructure with gain medium inside is theoretically studied to analyze the characteristic of plasmonic emitting with wide bandwidth. An accurate analytical model is built based on the transformation optics. In this model, the poles of the electrostatic potential function are in the second and the fourth quadrant of the complex plane if the imaginary part of the relative permittivity of the gain medium is larger than the loss compensation threshold, and then the extinction cross section is to be negative by integrating the electrostatic potential over the half complex plane via an inverse Fourier transform. The positive extinction cross section corresponds to absorption, and the negative corresponds to emission. The proposed analytical model agrees well with the numerical simulation results based on the finite element method, to give a physical insight into the loss compensation property of the plasmonic nanostuctures. Results show that the negative extinction cross section is realizable by introducing the gain medium into a plasmonic crescent nanowire, which is equivalent to an emitting device with wide bandwidth.