In this paper, we present the front-tracking-based results of containerless solidification of a liquid droplet with laminar forced convection. The droplet starts solidifying from a nucleus of solid phase assumed to be located at its bottom, and the phase change interface propagates through the droplet as time progresses. The problem is governed by various parameters such as the Reynolds number Re, the Prandtl number Pr, the Stefan number St, the Weber number We, the temperature of the surrounding fluid θin, volume change in terms of the solid-to-liquid density ratio ρsl, the growth angle ϕgr and the solidification nucleus size r0. We focus on small-sized droplets with low Re, and thus an axisymmetric configuration is used. Numerical results show that the presence of the forcing flow whose temperature below the solidifying point of the droplet liquid enhances the solidification process with a decrease in the solidification time, i.e. time for completion of solidification, with respect to an increase in Re from 20 to 200. However, variation of Re in this range does not affect much the shape of the solidified droplet. Similarly, the droplet shape after complete solidification is minor affected by Pr varied from 0.01 to 0.32, We varied from 0.05 to 6.4 or θin varied from −2.0 to 0. In contrast, the solidified droplet shape is strongly affected by St varied in the range of 0.025–1.6, ϕgr varied in the range of 0–28°, ρsl varied in the range of 0.8–1.2 or ksl varied in the range of 0.125–8.0 with an increasing in the droplet aspect ratio (or with a decrease in the top angle) with respect to a decrease in any of St, ρsl, ksl or with respect to an increase in ϕgr. However, the size of the nucleus normalized by the initial liquid droplet diameter, r0/D, changed from 0.08 to 0.15 has no effect on the solidified droplet shape. Concerning the solidification time, it increases with an increase in Pr, ϕgr, θin or with a decrease in St, ksl.