This paper proposes a novel high-gain millimeter-wave microstrip array antenna formed on a low temperature co-fired ceramic (LTCC) substrate. The proposed antenna employs alternately arranged parasitic elements formed on only two LTCC layers. This paper describes the design and characteristics of the proposed antenna. The antenna performance is also evaluated by electro-magnetic simulation. The proposed antenna achieves the antenna gain of 10.3 dBi and its radiation efficiency is greater than 60.3% at 60-GHz band. The proposed millimeter-wave antenna promises thin and compact antenna-integrated RF modules that provide a low-cost millimeter-wave system-on-package.