Linear stability of a steady convective motion of a viscous incompressible fluid in a circular pipe is considered in the paper. The steady motion is generated by internal heat sources with constant density uniformly distributed within the fluid. Both axisymmetric and asymmetric perturbations are analyzed. Linear stability problem is solved numerically for different values of the Prandtl number. It is found that the most unstable mode corresponds to the asymmetric perturbations with the azimuthal wave number n = 1. In contrast with linear stability problem for plane vertical layer, it is found that even for small Prandtl numbers, two modes of instability are present. Calculated linear stability characteristics are compared with available experimental data. Good agreement is found in terms of the form of the instability mode and the wavelength of the most unstable perturbation. Calculated critical Grashof numbers are higher than the corresponding experimental values.