Broccoli and fresh broccoli can be frozen but to keep the broccoli fresh before freezing you should blanch the broccoli before you put it in the freezer.
Blanching the fresh broccoli before freezing it helps to preserve the taste and the green color of the broccoli so that it is just as good tasting as it would be if you hadn't froze it.
Blanch the fresh broccoli in boiling water for at least 3 minutes or steam the broccoli for 5 minutes and they will be just fine when frozen.
If you fail to blanch the broccoli before freezing it the green color will usually go away and the broccoli won't taste as good as before.
I've blanched broccoli and have frozen broccoli for up to a year and it was still very good tasting.