This contribution presents, for the first time, the design of microwave lowpass filter with ultrawide stopband and low insertion loss based on the log-periodic zig-zag defected ground structure (DGS); the design is specifically evolved from the principle of the log-periodic line antenna and the slotline based DGS. Based on the log-periodic property, studies show that ultra-wideband suppression can be realized by increasing the flare angle or the angle subtended by each element of the slotline DGS. The developed filter therefore shows low insertion loss of 0.7 dB within the passband, sharp transition between the passband and the stopband and ultra-wide suppression band from 2.61-26.5 GHz with a 20 dB suppression level. The DGS architecture is simple and easy to realize, and the design is thus useful in many microwave applications. The fabricated prototype filter validates the study, both from simulations and from measurements.