Numerical simulations of the transmission performance of a recently proposed optical signal modulation technique, adaptively modulated optical orthogonal frequency division multiplexing (AMOOFDM), are undertaken in un-amplified multi-mode fibre (MMF)-based links using directly modulated DFB lasers (DMLs). It is shown that 28 Gb/s over 300 m and 10 Gb/s over 900 m transmission of intensity-modulation and direct-detection (IMDD) AMOOFDM signals at 1550 nm is feasible in DML-based links using MMFs with 3-dB effective bandwidths of as small as 150 MHz.km. Apart from a higher signal transmission capacity, AMOOFDM also has a greater spectral efficiency and is less susceptible to different launching conditions, modal dispersion and fibre types, compared with all existing schemes. In addition, a large noise margin of about 15 dB is also observed. The bits of resolution of analogue-to-digital converters and the cyclic prefix of AMOOFDM symbols are the main factors limiting the maximum achievable performance, on which the influence of DMLs is, however, negligible under the optimum operating condition.