In this project, to theoretically understand how a polymer chain extends in chain-growth polymerization at single-molecule perspective, we construct a one-dimensional model of a growing Rouse chain under tension so as to calculate the real-time chain length. One end of the chain is anchored and the second end is linked to a catalyst, which itself attached to a newly added bead. The bead is subject to a constant pulling force, and the solution contains monomers that add to the growing end of the chain. We calculate the exact end-to-end distance for the Rouse chain with a small number of beads to test the accuracy of approximations we made for evaluating long-time dynamics of a long polymer chain, with the goal of determining the dynamics of a growing polymer chain with any number of monomers.