In this work we theoretically study steady state thermoelectric transport through a single-molecule junction with a long chain-like bridge. Electron transmission through the system is computed using a tight-binding model for the bridge. We analyze dependences of thermocurrent on the bridge length in unbiased and biased systems operating within and beyond linear response regime. It is shown that length-dependent thermocurrent is controlled by the lineshape of electron transmission in the interval corresponding to HOMO/LUMO transport channel. Also, it is demonstrated that electron interactions with molecular vibrations may significantly affect length-dependent thermocurrent.