We present observations of the dwarf irregular galaxy NGC 4449 at 850 \mu m and 450 \mu m obtained with SCUBA at the JCMT . The distribution of the cold dust agrees well with that of the CO and H \alpha emission . To explain the integrated mm- through far-infrared continuum spectrum three dust components are required , with temperatures of 16 K , 39 K and 168 K , respectively . The dust mass is dominated by the cold dust component ; we derive a total dust mass of \sim 3.8 ~ { } \times~ { } 10 ^ { 6 } ~ { } M _ { \odot } , and with the local gas-to-dust ratio of \sim 130 a total gas mass of M _ { HI + H _ { 2 } } \sim 4.9 ~ { } \times~ { } 10 ^ { 8 } M _ { \odot } . Comparison with the HI mass leads to a total molecular gas mass of \sim 3.4 ~ { } \times~ { } 10 ^ { 8 } M _ { \odot } . We derive a conversion factor of the CO line intensity to molecular hydrogen column density X _ { CO } = N _ { H _ { 2 } } / I _ { CO } which is at least 11 times larger than the Galactic value . These values are in accord with the lower metallicity of NGC 4449 .