In this paper, a novel gamma-shadowed two-ray with diffuse power (GS-TWDP) composite fading model is proposed. The model is intended for modeling propagation in the emerging wireless networks working at millimeter wave (mmWave) frequencies, and is obtained as a combination of TWDP distribution for description of multipath effects and gamma distribution for modeling variations due to shadowing. After derivation of the exact probability density function (PDF), cumulative distribution function (CDF) and moment generating functions (MGF) expressions are obtained. Proposed model is verified by comparing the analytically obtained results with those measured at 28 GHz and reported in literature. Two upper bound average symbol error probability (ASEP) expressions are then derived for M-ary rectangular quadrature amplitude modulation (RQAM) by employing Chernoff and Chiani approximations of Gaussian Q-function, and are used to investigate relationship between GS-TWDP parameters and system performance. All the results are verified by Monte-Carlo simulation.