We study the minimum spanning tree (MST) construction problem in wireless networks under the physical interference model based on SINR constraints. We develop the first distributed (randomized) O(μ)-approximation algorithm for MST, with the running time of O(Dlogn) (with high probability) where D denotes the diameter of the disk graph obtained by using the maximum possible transmission range, and $\mu=\log{\frac{d_{max}}{d_{min}}}$ denotes the "distance diversity" w.r.t. the largest and smallest distances between two nodes. (When $\frac{d_{max}}{d_{min}}$ is n-polynomial, μ=O(logn).)