How to transmit data from MSP430F5529 through UART via USB cable to PC directly without using any serial to USB converter?

There is CDC open source example from TI USB stack that is used for USB communication with PC. Device will be enumerated as virtual com port and code on PC side is the same like for UART.

http://www.ti.com/tool/msp430usbdevpack

Do you have the LaunchPad? That board would have an UART/USB converter (called "backchannel UART" or "application UART") as an additional option.

I want to avoid the launchpad and use only MSP430F5529 IC with the PC.

I want to know if there is some functions/code to be burnt in MSP430F5529.

for ex, when using launchpad, data is transmitted when we put in UCA0TXBUF.
But now in which register data needs to be put, so that it will be transmitted to PC

Then you have to implement the basic USB protocol, and a CDC interface.

USB is rather complex; a simple register would not suffice. See zrno soli's answer.