The color "scheme" itself isn't a problem, it's more like being just the colors themselves, so if you want to keep the same thematic set of colors, just change the hues to something more muted (even if they are the same blues) that are easier on the eyes.
For example, the blue #0000CC that you use as a background can be painful on the eyes, but a more muted #336699 is much cooler and easier... you can match it with greens (#339999), whites (as you already do with your text), light blues (#66CCCC) and reds (#CC3333) and so on.. (those are colors matched directly from the color wheel, btw). Otherwise, if you insist on using those colors then it should be matched with the appropriate text colors too (which can reduce eyestrain, but barely, if at all).
You may even be interested in
www.colorschemer.com (everyone swears by it). Other than that, your site's on the right track and is a good one.
Hope that helps. Good luck!