In this paper, we propose a design utilizing two identically parallel-aligned nematic liquid crystal (LC) plates for fast-response and polarization-independent phase modulator. Driven by synchronized voltage signals, such a polarizer-free variable phase modulator shows a wide tunable range from zero to more than 3π, back and forth at 532nm. Due to the optical compensation of the two plates, the rise and fall time of the phase retardation corresponds to the switching-on time of the two plates. Several advantages are illustrated based on the optical compensation of two identical parallel-aligned plates. First, zero phase retardation is obtained, which overcomes the residual phase due to surfaced anchored liquid crystal molecules. The second advantage is sub-millisecond response of rise and fall of retardation since simultaneous relaxation of the two plates remains optically hidden during the synchronized voltages fall. This fast-response and polarization-independent phase modulator has great potential for practical use, including optical communications and light field imaging systems.