A method of fast laser frequency tuning and frequency modulation by electro-optical crystal is reported. Due to the electro-optical effect of LiNbO3 crystal, fast laser frequency tuning and modulation of the Littrow type external cavity diode laser(ECDL) with an electro-optical crystal is demonstrated by changing the effective laser cavity length with the voltage on the crystal. By this method, in the homemade ECDL, the tuning range of 350 MHz is achieved with tuning rate of 2 kHz, the tuning coefficient is about 1.06 MHz/V, and the effect of laser tuning was observed by saturated absorption spectrum. The fast frequency modulation can be used on the frequency stabilization. The dispersion signal of the saturated absorption spectrum of D2 line of 87Rb atoms is achieved with the laser frequency modulation rate of 5～100 kHz, and the laser frequency is long-term stabilized on the peak and cross peak of saturated absorption spectrum of the D2 line of 87Rb atoms.