Greedy forward routing (abbreviated by GFR) in wireless ad hoc networks is a localized geographic routing in which each node discards a packet if none of its neighbors is closer to the destination of the packet than itself, or otherwise forwards the packet to the neighbor closest to the destination of the packet. If all nodes have the same transmission radii, the critical transmission radius for GFR is the smallest transmission radius which ensures that packets can be delivered between any source-destination pairs. In this paper, we study the asymptotic critical transmission radius for GFR in randomly deployed wireless ad hoc networks. We assume that the network nodes are represented by a Poisson point process of density n over a convex compact region of unit area with bounded curvature. Let β 0 = 1/ (2/3 - √3/2π) ≈ 1.6 2. We show that √β 0 ln n/πn is asymptotically almost surely (abbreviated by a.a.s.) the threshold of the critical transmission radius for GFR. In other words, for any β > β 0, if the transmission radius is √β ln n/πn, it is a.a.s. packets can be delivered between any source-destination pairs; for any β < β 0, if the transmission radius is √β ln n/πn, it is a.s.s. packets can't be delivered between some source-destination pair.