The first law of thermodynamics for the three horizons of Reissner-Nordstr(o)m quintessence (RNQ) spacetime is obtained.For a general process of RNQ spacetime,the expressions for the radius changes of the three horizons are derived.When only mass changes,the heat fluxes through the three horizons are equivalent and no heat is left in the black hole region.Finally,a further discussion on the thermal properties of an RNQ black hole is given.Black holes satisfy the four laws of thermodynamics,which indicates a deep connection between gravity and thermodynamics,[1-4] where the entropy of black hole is proportional to the area of event horizon and the temperature of black hole is proportional to the surface gravity of event horizon.For a static and spherically symmetric spacetime,the field equation may be written as the first law of thermodynamics.[5-10]