A near-optimal design of a log-periodic dipole array (LPDA), suitable for digital video broadcasting-terrestrial (DVB-T) reception (470-790 MHz), is presented. The LPDA is required to provide low standing wave ratio as well as high-gain radiation pattern with sufficient gain flatness over the entire passband, and concurrently achieve low gain for frequencies above 800 MHz to reject LTE800 signals and thus improve the reception quality in the DVB-T band. All the above requirements are better satisfied by applying a novel particle swarm optimization (PSO) variant, called PSO with velocity mutation (PSOvm). PSOvm induces mutation on the velocities of those particles, which are unable to improve their fitness. As shown in this paper, PSOvm comes closer to the above requirements compared to four well-known optimization methods and outperforms the traditional LPDA design method proposed by Carrel. The LPDA geometry chosen for optimization is not the conventional one, and therefore the dipoles are not considered to be included inside a specified angle as proposed by Carrel. Thus, the dipole lengths and distances as well as the boom dimensions are independently optimized. The PSOvm-based LPDA sufficiently meets all the above requirements and thus is suitable for DVB-T reception without the use of an external LTE-band rejection filter.