< ：TI_MSP430_内容页_SA7 --> 你通过串口给单片机发送字符'a'了吗？
可以用仿真器仿真啊，遇到问题的最好解决方法就是仿真。

你都说别人可以了啊，那问题是，器件型号一样不？还有你说不行，现象是啥？？

将P1.1 和 P1.2 短接，试试下面的代码，我试了LED会有交替闪烁

#include "msp430g2553.h"
  
#define TXLED BIT0
#define RXLED BIT6
#define TXD BIT2
#define RXD BIT1
  
const char string[] = { "Hello World " };
unsigned int i; //Counter
  
int main(void)
{
   WDTCTL = WDTPW + WDTHOLD; // Stop WDT
   DCOCTL = 0; // Select lowest DCOx and MODx settings
   BCSCTL1 = CALBC1_1MHZ; // Set DCO
   DCOCTL = CALDCO_1MHZ;
   P2DIR |= 0xFF; // All P2.x outputs
   P2OUT &= 0x00; // All P2.x reset
   P1SEL |= RXD + TXD ; // P1.1 = RXD, P1.2=TXD
   P1SEL2 |= RXD + TXD ; // P1.1 = RXD, P1.2=TXD
   P1DIR |= RXLED + TXLED;
   P1OUT &= 0x00;
   UCA0CTL1 |= UCSSEL_2; // SMCLK
   UCA0BR0 = 0x08; // 1MHz 115200
   UCA0BR1 = 0x00; // 1MHz 115200
   UCA0MCTL = UCBRS2 + UCBRS0; // Modulation UCBRSx = 5
   UCA0CTL1 &= ~UCSWRST; // **Initialize USCI state machine**
   UC0IE |= UCA0RXIE; // Enable USCI_A0 RX interrupt
  UCA0TXBUF ='a';
   __bis_SR_register(CPUOFF + GIE); // Enter LPM0 w/ int until Byte RXed
   while (1)
   { }
}
  
#pragma vector=USCIAB0TX_VECTOR
__interrupt void USCI0TX_ISR(void)
{
   P1OUT |= TXLED;
     UCA0TXBUF = string[i++]; // TX next character
    if (i == sizeof string - 1) // TX over?
       UC0IE &= ~UCA0TXIE; // Disable USCI_A0 TX interrupt
    __delay_cycles (100000);
    P1OUT &= ~TXLED; }
   
#pragma vector=USCIAB0RX_VECTOR
__interrupt void USCI0RX_ISR(void)
{
   P1OUT |= RXLED;
    if (UCA0RXBUF == 'a') // 'a' received?
    {
       i = 0;
       UC0IE |= UCA0TXIE; // Enable USCI_A0 TX interrupt
      UCA0TXBUF = string[i++];
    }
    __delay_cycles (100000);
    P1OUT &= ~RXLED;
}

做了3点变化
1.在进入低功耗之前手动发送了‘a'
即   UCA0TXBUF ='a';

2.3.熄灭LED之前加入了延时
__delay_cycles (100000);