We investigate the nonclassicality and decoherence of a photon-subtraction-addition coherent state (a++a)m|a in a thermal environment. Its nonclassicality is discussed by deriving analytically Mandel's Q parameter, photon number distribution, and Wigner function. It is shown that if the condition |2z*+ -*|2 1 is satisfied, the Wigner function always presents the negativity for the one-order photon-subtraction-addition coherent state (m=1). Based on the evolution formula of Wigner function, we derive a compact expression for Wigner function in the thermal environment. It is found that when t(1/2)ln(2N+2)/(2N+1) there is no negativity for the case of m=1. In addition, the evolution of nonclassicality is discussed in terms of the negative volume of Wigner function.