IS there any Equivalent for Windows API in LInux???

The UNIX equivalent to Win32 API is POSIX.

"With UNIX, there is almost a 1-to-1 relationship between the system calls (e.g., read) and the library procedures (e.g., read) used to invoke the system calls. In other words, for each system call, there is roughly one library procedure that is called to invoke it...Furthermore, POSIX has only about 100 procedure calls."
"With Windows, the situation is radically different. To start with, the library calls and the actual system calls are highly decoupled...The number of Win32 API calls is extremely large, numbering in the thousands. Furthermore, while many of them do invoke system calls, a substantial number of them are carried out in userspace."

"Modern Operating Systems" 2nd ed. by Andrew S. Tanenbaum. 2001, Prentice Hall, Inc. pp.54

If you are looking to port Win32 API code to Linux, take a look at Wine.