In this paper, a new design of a low-profile and multilayer broadband microstrip antenna is proposed for millimeter-wave applications at 60 GHz. The antenna is a metamaterial inspired structure that consists of a non-uniform octagon shape radiating element on the top of six layers of substrate and a periodic structure at the second layer. The proposed antenna geometry is designed using Low Temperature Co-Fired Ceramic (LTCC) technology for 3D multilayer vertical integration. This antenna achieves 24.16 % of bandwidth ranging from 55.5 GHz to 70 GHz, with a peak gain of 5.1 dBi at 60 GHz. HFSS is used for design and simulation of this LTCC based broadband antenna. Three prototypes are fabricated for measurement and a good agreement of numerical and practical results is obtained which makes this antenna very attractive for the use in future wireless communication systems.