In this paper, we consider the one-dimensional porous-elasticity system with indefinite damping mechanism of type given by τ(x) (possibly changing sign) acting only in the equation for the volume fraction and we prove that the system is exponentially stable under particular relationship between coefficients of system and provided τ¯=∫0Lτ(x)dx>0 and ‖τ−τ¯‖L2<ϵ for ϵ small enough. The decay rate will be described explicitly for constant damping. Our approach is inspired in the work due to Muñoz Rivera and Racke (Journal of Mathematical Analysis and Applications, 341, 1068–1083. 2008) and we prove that the system has the spectrum determined growth (SDG).