Parametric generation of oscillations and waves is a paradigm, which is known to be realized in various physical systems. Unique properties of quantum semiconductor superlattices allow us to investigate high-frequency phenomena induced by the Bragg reflections and negative differential velocity of the miniband electrons. Effects of parametric gain in the superlattices at different strengths of dissipation have been earlier discussed in a number of theoretical works, but their experimental demonstrations are so far absent. Here, we report on the first observation of the dissipative parametric generation in a subcritically doped GaAs/AlGaAs superlattice subjected to a dc bias and a microwave pump. We argue that the dissipative parametric mechanism originates from a periodic variation of the negative differential velocity. It enforces excitation of slow electrostatic waves in the superlattice that provide a significant enhancement of the gain coefficient. This work paves the way for a development of a miniature solid-state parametric generator of GHz-THz frequencies operating at room temperature.