Electrical discharge machining (EDM) is a machining process transforming electric energy into thermal energy to remove materials. The current impulse is a very important factor for machining characteristics of EDM. A series of experiments were performed to investigate the influence of current impulse on machining characteristics. The features of current impulse have initial current, current rising slope and impulse pattern. The used patterns of current impulse included rectangular current impulse, trapezoidal current impulse and the $1^{st}$ order current impulse. The machining characteristics are associated with relative wear ratio (RWR) and material removal rate (MRR). Experimental showed that using trapezoidal current impulse with small initial current or little current rising slope reduced relative wear ratio and material removal rate as well. However, larger relative wear ratio was obtained for workpiece of tungsten carbide when current rising slope was too little. Using the $1^{st}$ order current impulse with $20;{mu}s$ current rising time can improve relative wear ratio about 30 % while remain material removal rate the same as rectangular current impulse for tungsten carbide.