In this paper, we address the problem of model reduction by moment matching for quadratic-bilinear time-delay systems. The moment of such systems is characterized by a power series representation, which can be computed by solving an infinite-dimensional system of Sylvester-like equations. A family of parameterized reduced-order models that preserves the quadratic-bilinear time-delay structure is derived through matching an approximate moment defined by truncating the power series. The developed theory is demonstrated on a numerical example.