An improved adaptive beamforming technique of antenna arrays is introduced. The technique is implemented by using a novel Invasive Weed Optimization (IWO) variant called Adaptive Dispersion Invasive Weed Optimization (ADIWO) where the seeds produced by a weed are dispersed in the search space with standard deviation specified by the fitness value of the weed. The adaptive seed dispersion makes the ADIWO converge faster than the conventional IWO. This behavior is verified by applying both the ADIWO and the conventional IWO on well-known test functions. The ADIWO method is utilized here as an adaptive beam former that makes a uniform linear antenna array steer the main lobe towards the direction of arrival (DoA) of a desired signal, form nulls towards the respective DoA of several interference signals and achieve low side lobe level (SLL). The proposed ADIWO based beamformer is compared to a Particle Swarm Optimization (PSO) based beamformer and a well known beamforming method called Minimum Variance Distortionless Response (MVDR). Several cases have been studied with different number of interference signals and different power level of additive zero-mean Gaussian noise. The results show that the ADIWO provides sufficient steering ability regarding the main lobe and the nulls, works faster than the PSO and achieves better SLL than the PSO and MVDR.