In this paper, a novel locally resonant structure with composite units is proposed. Formation mechanisms and low-frequency characteristics of the band gaps in the proposed structure are investigated using finite element methods. Frequency positions of band gaps depend on natural frequencies of the corresponding locally resonant modes. And the gap width is related to both the Q factor of the locally resonant modes and the interaction strength in-between the locally resonant structural units. Phononic crystal structures with composite units exhibit multiple resonances and band gaps in low-frequency range, depending on the arrangement of locally resonant units. Due to the mode degeneracy of the vertical and horizontal local resonances, the composite structures possess band gaps below 200Hz with the total gap width more than 60% and the lowest frequency down to 18Hz. The structures and results provide a new effective method for phononic crystal structures to obtain broadband gaps in low-frequency range.