Quasi-one-dimensional (1D) materials provide a superior platform for characterizing and tuning topological phases for two reasons: (i) existence for multiple cleavable surfaces that enables better experimental identification of topological classification and (ii) stronger response to perturbations such as strain for tuning topological phases compared to higher dimensional crystal structures. In this paper, we present experimental evidence for a room-temperature topological phase transition in the quasi-1D material Bi4I4, mediated via a first-order structural transition between two distinct stacking orders of the weakly coupled chains. Using high-resolution angle-resolved photoemission spectroscopy on the two natural cleavable surfaces, we identify the high-temperature β phase to be the first weak topological insulator with two gapless Dirac cones on the (100) surface and no Dirac crossing on the (001) surface, while in the low-temperature α phase, the topological surface state on the (100) surface opens a gap, consistent with a recent theoretical prediction of a higher-order topological insulator beyond the scope of the established topological materials databases that hosts gapless hinge states. Our results not only identify a rare topological phase transition between first-order and second-order topological insulators but also establish a novel quasi-1D material platform for exploring unprecedented physics.