That image has very soft edges, plus some JPEG artifacts. (Zoom in on the edges and see.) Was it scanned-in or photographed? If so you need to do some posterisation in Photoshop or some other bitmap package first. If it was rendered from vector artwork, you need to render it in non-anti-aliased to convert it to a GIF.
You want it so that when you zoom in on the edges you see that all the "white" pixels really are white, and all the "red" pixels are the same solid red.
Alternatively, you could convert the existing anti-aliased image into a PNG with alpha-channel; this will look better than a GIF on the browsers which support it (Mozilla, Firefox, Galeon, Safari etc) but not on the one which doesn't support it (Internet Explorer).
Peter