Broadband achromatic metalens imaging is of great interest in various applications, such as integrated imaging and augmented/virtual reality display. Current methods of achromatic metalenses mainly rely on the compensation of a linear phase dispersion implemented with complex nanostructures. Here, we propose and experimentally demonstrate a polarization-insensitive achromatic metalens (PIA-ML) based on computational wavefront coding. In this method, simple circular or square nanopillars are individually coded such that the focal depths at wavelengths at both ends of the achromatic bandwidth overlap at the designed focal plane, which removes the limitation of requiring a linear phase dispersion. An optimized PIA-ML that works in the full optical communication band from 1300 to 1700nm was obtained using a particle swarm optimization algorithm. Experimental results show that both focusing and imaging of the fabricated metalens are consistent with theoretical predictions within the broadband wavelength range, which provides a new methodology for ultra-broadband achromatic imaging with simple-shaped nanostructures.