We used a multichannel extension of the Schwinger variational principle [K. Takatsuka and V. McKoy, Phys. Rev. A 24, 2473 (1981)] to study the cross sections for excitation of the X 1 g+b u+3, a g+3, and c3 u transitions in H2 by low-energy electrons. These cross sections were obtained with two open channels for each transition and for energies near threshold to 30 eV. The results for the b3u+ and a g+3 states agree quite well with available experimental data. However, the cross sections for excitation of the c u3 state differ significantly from the measured values at the two energies, 20 and 30 eV, where data are available.