How do I write FileReader test in Jasmine?

The problem here is the use of reader.onload which is hard to test. You could use reader.addEventListener instead so you can spy on the global FileReader object and return a mock:

eventListener = jasmine.createSpy();
spyOn(window, "FileReader").andReturn({
 addEventListener: eventListener
})

then you can fire the onload callback by yourself:

expect(eventListener.mostRecentCall.args[0]).toEqual('load');
eventListener.mostRecentCall.args[1]({
  target:{
    result:'the result you wanna test'
  }
})

This syntax changed in 2.0. Code below gives an example based on Andreas Köberle's answer but using the new syntax

    // create a mock object, its a function with some inspection methods attached
    var eventListener = jasmine.createSpy();

    // this is going to be returned when FileReader is instantiated
    var dummyFileReader = { addEventListener: eventListener };

    // pipe the dummy FileReader to the application when FileReader is called on window
    // this works because window.FileReader() is equivalent to new FileReader()
    spyOn(window, "FileReader").and.returnValue(dummyFileReader)

    // your application will do something like this ..
    var reader = new FileReader();

    // .. and attach the onload event handler
    reader.addEventListener('load', function(e) {

        // obviously this wouldnt be in your app - but it demonstrates that this is the 
        // function called by the last line - onloadHandler(event);
        expect(e.target.result).toEqual('url');

        // jasmine async callback
        done();
    });

    // if addEventListener was called on the spy then mostRecent() will be an object. 
    // if not it will be null so careful with that. the args array contains the 
    // arguments that addEventListener was called with. in our case arg[0] is the event name ..
    expect(eventListener.calls.mostRecent().args[0]).toEqual('load');

    // .. and arg[1] is the event handler function
    var onloadHandler = eventListener.calls.mostRecent().args[1];

    // which means we can make a dummy event object .. 
    var event = { target : { result : 'url' } };

    // .. and call the applications event handler with our test data as if the user had 
    // chosen a file via the picker
    onloadHandler(event);