Chemical modification can effectively control the quantum spin Hall (QSH) state by changing the lattice constant or topological phase transition. We functionalized ultraflat stanene with hydrogen and halogens on a single side (s-SnX) and both sides (b-SnX). It was found that the buckled heights of the neighboring Sn atoms for s-SnX were still zero, while b-SnX changed into a buckled structure, which is consistent with previous studies. In this work, the electronic and topological properties of s-SnX (X = H, F, Cl, Br, I) were mainly studied based on first-principles calculations. We predicted that s-SnF, s-SnCl and s-SnBr would be topological insulators (TIs). It was found that the band structures of s-SnF, s-SnCl, s-SnBr have s-p band inversions and semimetal-to-semiconductor transitions considering spin orbit coupling (SOC) with the largest band gap of 0.25 eV. The edge bands of calculating the edge states cross linearly, and the numbers of edge bands passing through the zero energy level between –X and Γ point are odd, indicating that s-SnF, s-SnCl and s-SnBr are TIs. Ultraflat stanene functionalized by hydrogen and halogen atoms can effectively control QSH states. It is proved that functionalization provides more choices for topological insulator materials and topological device applications.