For now I have not any real project experience. I want apply for an internship next summer. What kind of C++ project should I program to add some value to me for applying an internship ? better not be large,just within 1500 lines code. better not with complex ui design. could you recommend some to me?

Here is a brainstorming list that comes to my mind respecting your 1500 loc :
- A * algorithm
- Dining philosophers
- List class implementation
- Vector class implementation
- Behaviour tree class
- Binary tree class
- Hash table class
- Simple UDP or TCP applications (server and client) just send a message (socket)
- Tower of Hanoi
- Fibonacci , Exponential , PI approximation recursive methods
- Tic Tac Toe
- Password/Username authentification
- Classes using virtual methods and pure virtual methods
- Implement Visitor pattern , Observer pattern , Factory pattern
- Implement Allocator class
- Implement Pool class
- Read from / Write to a binary file
- Read from / Write to an XML file
- Read from / Write to a JSON file
- Parse a file to an application that will create instances (of whatever) based on the content of the file

Is this enough , does it contains some highlights ? :)