The Japanese X-ray satellite ASCA observed NGC 1808, which is known to exhibit both Seyfert and starburst activities. In the soft X-ray band, ASCA detected emission lines from highly ionized Mg and Si, which confirmed the presence of a thin thermal plasma, due possibly to starburst activity. The thin thermal plasma consists of two temperature components of kT similar to 0.78 keV and kT similar to 0.35 keV. We found that the intrinsic absorption toward the 0.78 keV plasma is N-H similar to 7 x 10(21) cm(-2), which is greater than the galactic foreground value of 2.8x10(20) cm(-2) (Dickey; Lockman 1990, AAA 53.155.163). This result implies that most of the X-ray emission from this plasma comes from the central region. The absorption toward the 0.35 keV plasma, on the other hand. shows a low value compared to the galactic absorption. This indicates that the plasma is more extended like an X-ray halo. The metal abundance of about 1 solar value found in the thin thermal plasma is larger than that of the archetypical starburst galaxy M82. In addition to the thin hot plasma, ASCA detected a hard X-ray component from NGC 1808, with a luminosity of 2X10(40) erg s(-1) (0.5-10 keV band), obscured by an absorbing column of 1.0x10(22) cm(-2). The hard X-ray flux and spectrum may also be attributable to starburst activity. However, the hard X-rays exhibited a long-term variability from the Ginga and ASCA observations, suggesting the presence of a low-luminosity AGN in NGC 1808.