2 Cisco 3750 switches are connected via port 22(Trunk). First switch consists of 3 VLANs(each vlan have 7 ports such as 1-7,8-14,15-21) and 2nd switch consists of 2 VLANs. what solution can i use to increase the bandwidth between the two switches without rewiring?
The bandwidth on an interface is the bandwidth on the interface. It is possible to use multiple interfaces (up to eight) in a port channel between the switches to give you a greater aggregate bandwidth, but a single flow will still only use a single link in the channel.
This will require more links between the switches, but you have not given enough information to determine if that requires the rewiring that you want to avoid.
Even the non-G, Fast Ethernet models feature SFP ports at gigabit speed. Those require running a fiber in between or alternatively, using 1000BASE-T transceivers that only need Cat-5e cabling - I believe GLC-T would fit.
If you're already on gigabit, the only alternatives are either aggregating multiple ports as Ron's described or replacing the switches with faster models.