This work investigates a polarization-independent and fast response microlens array. This array is composed of a concave polymer microlens array and blue phase liquid crystals (BPLCs). The microlens array can be either positive or negative, depending on the birefringence of the BPLCs. The experimental results show that the microlens array is fast switched between positive and negative focal lengths via controlling the electric fields, and the response time is a few hundred microseconds. Additionally, the focusing efficiency is independent of the polarization of the incident light.