Observational data suggest that a belt of planetesimals is expected close to the snow line in protoplanetary disks. Assuming there is such a belt in TRAPPIST-1 system, we examine possibilities of water delivery to the planets via planetesimals from the belt. The study is accomplished by numerical simulations of dynamical evolution of a hypothetical planetesimal belt. Our results show that the inner part of the belt is dynamically unstable and planetesimals located in this region are quickly scattered away, with many of them entering the region around the planets. The main dynamical mechanism responsible for the instability are close encounters with the outermost planet Trappist-1h. A low-order mean-motion resonance 2:3 with Trappist-1h, located in the same region, also contributes to the objects transport. In our nominal model, the planets have received non-negligible amount of water, with the smallest amount of 15% of the current Earth’s water amount (EWA) being delivered to the planet 1b, while the planets Trappist-1e and Trappist-1g have received more than 60% of the EWA. We have found that while the estimated efficiency of water transport to the planets is robust, the amount of water delivered to each planet may vary significantly depending on the initial masses and orbits of the planets. The estimated dynamical ,,half-lives” have shown that the impactors’ source region should be emptied in less then 1 Myr. Therefore, the obtained results suggest that transport of planetesimals through the system preferably occurs during an early phase of the planetary system evolution.