I would say it sounds just a little off. A couple of things to address:
(1) Is the 'ancient country' a country that existed in the past and does not exist anymore? If so, the past tense would be required.
(2) 'only depends on planting' <- this section is where it gets a little awkward. First, it would feel more natural if the 'only' and 'depends' were switched around to read 'depends only on planting...'. Second, 'only' sometimes carries the meaning/nuance of sufficiency/simplicity ("It's only 2 hours away, so close!"), while what you want to express--indeed emphasize here is the single factor on which the economy of this country depends. In which case 'solely' rather than 'only' emphasizes that a little better.
There, your sentence is up to snuff, and I've read much worse from native speaker college graduates.
If we were to nitpick more though:
-'rich' and 'diversity' sound a little repetitive--after all, it's not like the 'diversity' of crops would be 'poor', right?
-Avoiding 'the X of Y' formulations in favor of 'Y's X' formulations are considered by some to be a better form of expression. So saying 'This ancient country's economy' rather than 'the economy of this ancient country'. This isn't a set rule though, it depends on what you want to emphasize, and your style of writing.
-Making the last idea 'planting a rich diversity of crops....' into a phrase without a verb sounds more natural for some reason to me.
Putting this all together, we get a couple of slightly more natural sentences:
-The economy of this ancient country depends only on planting a diversity of crops
-The economy of this ancient country depends solely on the diversity of its agricultural production
-This ancient country's economy depends solely on the diversity of its agricultural production