All-optical buffers have been considered as essential components for all-optical communications. Considering the requirements of controllable optical delay lines and optical buffers, the external dynamic tuning of slow light in photonic crystal waveguides has been studied. A novel photonic crystal waveguide on polymer substrate is proposed. Numerical study using plane, wave expansion method shows that this structure supports a single guided mode transmission,which allows a low group velocity of 10-2c in the vicinity of band edge. Since the substrate material possesses a high electro-optic coefficient and a subpicosecond nonlinear response time, and local field effect induced the by slow light transmission can enhance electro-optic effect greatly, these properties offer the opporunity to tune the slow light mode in wide frequency range with low power. Numerical analysis shows that by applying an external voltage of 80 V, the guided mode will shift 80.8 nm, and moreover the wavelength shift is nearly linearly increased with the increas of applied modulated voltage. Modulation sensitivity is about 1 nm/V. The flexible dynamical tuning of slow light mode can meet the requirements for the use of optical buffer in all-optical network in principle.