hosta(eth0)----|switch|---(eth0)hostb

say hosta and hostb both connect to a swtich using eth0 with public IP addresses, and I add secondary and private IP on hosta and hostb's same eth0 interfaces.

So in order for them to reach each other, do I need to config the switch?

No, you (in general) need to only configure IP routing in the computers, not the switches.

i think as long as the two host use IPs from same subnet block, there is no need to config anything besides IP address, right?

Well, it is not clear what you are trying to accomplish, it is not clear by what you mean by 'private', it is not clear where your Internet gateway resides in your drawing, it is not clear what routing protocol(s) you are using, and it is not clear if you are planning to use network address translation (NAT).... so in other words, to answer your question correctly, we need more details :-)