We calculate the nucleon-nucleon scattering amplitudes in the 1S0 and 3S1−3D1 channels at next-to-next-to-leading order starting from a recently proposed nonrelativistic chiral effective theory, which includes dibaryon fields as fundamental degrees of freedom. We restrict ourselves to center-of-mass energies (E) smaller than the pion mass (mπ) and further divide the calculation into two relative momentum (p) regions, a high-energy one p~mπ≫δmi, δmi being the dibaryon residual masses, and low-energy one p≲δmi. We first match to a lower energy effective theory in which we calculate the amplitudes in the high-energy region. We further match this effective theory to the so-called pionless effective theory in the low-energy region and carry out the calculations in the latter. Dimensional regularization and minimal subtraction scheme are used throughout. For 1S0 channel a good description of the phase shift data is obtained for E≲50 MeV. For the 3S1−3D1 channel, the 3S1 phase shift data is only well described up to E≲20 MeV.