We have demonstrated spin pumping from a paramagnetic state of an insulator La2NiMnO6 into a Pt film. Single-crystalline films of La2NiMnO6 which exhibit a ferromagnetic order at TC ~ 270 K were grown by pulsed laser deposition. The inverse spin Hall voltage induced by spin-current injection has been observed in the Pt layer not only in the ferromagnetic phase of La2NiMnO6 but also in a wide temperature range above TC. The efficient spin pumping in the paramagnetic phase is ascribable to ferromagnetic correlation, not to ferromagnetic order.