It most certainly will! It happens when it runs out of fuel (hyrdogen) and starts to expand outwards, this ‘exploding’.
Our sun will become a red giant in approximately 5 billion years. It hasn’t become one yet as it is right in the middle of its life-cycle, it has plenty of hydrogen to fuel it so it won’t go anytime soon!
The sun is a relatively small star and there are scientists who do not think it will explode, I have found a nice website which explains this, and I copied and pasted this sentence from it
“What will happen is that the Sun will just blow off its outer layers leaving a carbon rich white dwarf core. It will cool down over billions of years until it reaches the very same temperature as with the universe”