Considering a small-scale fading environment in a dense random wireless network, we investigate the impact of the carrier-sensing threshold on the link performance under the premise of a fixed carrier-sensing range. At first, we assume a close transmitter-receiver distance and model the network nodes as a homogeneous Poisson point process (PPP). Then we present a simple analysis model of the conditional link success probability to establish a correlation between the interference capture and the link success. Subsequently, based on the assumption that the interference among proximity nodes mainly comes from the nearby nodes, we obtain the bounds of the carrier-sensing threshold through stochastic analysis and a simple adaptive algorithm to adjust the carrier-sensing threshold within its bounds is further presented. Numerical results show that the proposed method enables the pending transmitter to adjust the bounds of the carrier-sensing threshold adaptively when the channel pathloss exponent changes and the validity of the proposed adaptive algorithm is verified in the simulations.