Species are threatened by climate changes, unless their populations have the ability to invade landscapes to search for new regions of suitable climate and conditions. It is therefore of utmost importance for ecologists to estimate the invasion time, as it is a crucial parameter used for environmental planning and may even determine survivability of the species. From a computational perspective, estimating the invasion time by running simulations is very time consuming, as the full model is based on a Markov Chain of exponential number of states with respect to the landscape size; therefore, in practice, this method is not suitable especially in case of frequent environmental changes or for environmental planning. In this paper, we propose a new way to estimate the time of invasion process using a powerful computational approach based on conductance and network flow theory. More specifically, we give a new formula for estimating the invasion time using a combination of network flow methodologies, and prove asymptotic bounds on the quality of the obtained approximation. The proposed approach is analyzed mathematically and applied to real heterogeneous landscapes of the United Kingdom to estimate the duration of the process; the theoretical bounds obtained are compared with simulation results. The evaluations of the proposed approach demonstrate its accuracy and efficiency in approximating the invasion time.