Linear stability of a convective motion in a tall vertical annulus is analyzed in the paper. The base flow is generated by a non-linear heat source. The base flow velocity and temperature distributions are obtained numerically solving the system of the Navier-Stokes equations under the Boussinesq approximation. Linear stability problem is solved for axisymmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results show that there are three destabilizing factors: (1) the increase of the gap between the cylinders, (2) the increase of the Frank-Kamenetsky parameter characterizing the rate and intensity of a chemical reaction and (3) the increase of the Prandtl number.