The shot noise of current through a metallic double quantum dot structure exhibiting negative differential conductance is studied. We can exactly solve the master equation and derive an analytical expression of the spectral density of current fluctuations as a function of frequency in the first Coulomb staircase region. For a large range of bias voltage the noise is calculated by Monte Carlo simulation. We show that the noise is always sub-Poissonian though it is considerably enhanced in the negative differential conductance regime.