Mode-division multiplexing (MDM), which employs the spatial modes of light as information carriers, has been widely investigated to increase the transmission capacity. Few-mode fibers (FMFs) and multi-mode fibers (MMFs) have been used for MDM fiber transmission. One of the MDM techniques known as twisted light multiplexing using orbital angular momentum (OAM) modes has recently attracted increasing interest. In this Letter, by splicing two FMFs together with a conventional OM3 MMF, we propose and demonstrate OAM-based MDM in a heterogeneous fiber-optic network, i.e., two OAM mode (OAM01 and OAM-11) multiplexing transmission in the heterogeneous FMFs and MMF network. We transmit 20-Gbit/s quadrature phase shift keying signals over two OAM modes in different mode groups without multiple-input multiple-output equalization techniques and achieve less than 2.8 dB optical signal-to-noise ratio penalties at a bit-error rate of 2×10-3. The experimental results show favorable transmission performance of OAM-based MDM in heterogeneous FMFs and MMF network compared to the one in FMF.