A two-dimensional (2D) optimized nanotaper mode converter is presented and analyzed using the finite-difference time-domain (FDTD) method. It can convert the mode size in a silicon pillar waveguide (PWG) from 4 \mum to 1 \mum over a length of 7 \mum and achieve a transmission efficiency of 83.6% at a wavelength of 1.55 \mum. The dual directional mode conversion of the nanotaper and its ability to perform mode compression and expansion are also demonstrated. The broadband with high transmittance is satisfied in this structure. Using this silicon-based nanotaper, mode conversion between integrated photonic devices can be more compact and efficient.