New far ultraviolet imaging of the galaxy NGC 205 is presented, which shows the emission is significantly offset ($\sim5^{\prime\prime}$ NW) from the optical and infrared centers of the galaxy. Spectral energy distribution (SED) modelling is applied to investigate the spatial dependence of the star formation history (SFH) of NGC 205, using data from far ultraviolet to far infrared. The SED model includes young and old stellar populations, gas emission, dust emission and dust absorption. The old stellar population has a total mass of $1.1\times10^8$ M$_{\odot}$ whereas the young population has a much smaller total mass of 3 200 M$_{\odot}$. The best forms of SFH for old and young stars are found to be exponentially declining bursts with start times $t_0$ yr ago and e-folding times $\tau$ yr. The old stellar population has uniform $t_0$ = 9.5 Gyr, with $\tau$ decreasing with radius from 1 Gyr to 500 Myr. The young stellar population has $t_0$ = 900 Myr and $\tau$ = 800 Myr, both uniform across NGC 205. The young and old stellar mass surface densities are exponential in radius with scale lengths of 40 and 110 pc, respectively. The dust heating has a $\sim$ 40% contribution from young stars and $\sim$ 60% from old stars.