Does this lens work on nikon d3000?

Tamron AF 18-200mm f/3.5-6.3 XR Di II LD Aspherical (IF) Macro Zoom Lens with Built In Motor for Nikon Digital SLR

If it has a built-in auto-focus motor, then yes.

Don't however expect much in the way of "macro" performance.

Macro lenses are prime lenses and are flat field lenses to prevent distortion at the edges of the image frame

One claim that Nikon can make that Canon can't is that the bayonet for the lens has not changed over the years. The bayonet is the mechanical device that physically connects the lens to the camera body.

I have a D7000 and have many old lenses. They all fit physically. Some of the lenses' bells and whistles (for example, the auto focus and auto exposure) do not function. However, I can still take the shot using manual settings.

Best wishes!