want to child object facing to camera

Somehow I solve this prebrem.

Save the direction to child object facing camera.

 defaultDirToCam = (Camera.main.transform.position - parent.position).normalized;
 defaultDirToCam.y = 0.0f;
 defaultEuler = transform.eulerAngles;

then, on update method,

 // object direction to camera
 Vector3 parentDirToCam = (Camera.main.transform.position - parent.position).normalized;
 // relative to camera position
 Vector3 relativePosition 
     = parent.InverseTransformPoint(Camera.main.transform.position);
 // differential y-axis
 float yDiffDeg 
     = Vector3.Angle( defaultDirToCam, new Vector3(parentDirToCam.x, 0.0f, parentDirToCam.z) );
 // differential x-axis
 float xDiffDeg
     = Vector3.Angle( -Vector3.forward, new Vector3(0.0f, parentDirToCam.y, defaultDirToCam.z) );
 // direction check
 if ( relativePosition.x < 0.0f ) {
     yDiffDeg = -yDiffDeg;
 }
 if ( relativePosition.y < 0.0f ) {
     xDiffDeg = -xDiffDeg;
 }
 // Relative to default rotation
 transform.rotation = Quaternion.Slerp( 
     transform.rotation,
     Quaternion.Euler( defaultEuler.x, defaultEuler.y + yDiffDeg, defaultEuler.z + xDiffDeg ),
     Time.deltaTime * chaseCameraSpeed);

I was able to solve it by this above code.

thanks.

You're making some mistakes here: transform.LookAt may receive a Transform or a position as argument, not a direction vector, thus you should use transform.LookAt(Camera.main.transform) or transform.LookAt(Camera.main.transform.position).
Your Slerp is also wrong, because you should pass a Quaternion as the target rotation, not a vector: use the vector to find the rotation with Quaternion.LookRotation, then pass this rotation as the 2nd argument, like this:

 var targetRot = Quaternion.LookRotation(Camera.main.transform.position - transform.position);
 transform.rotation = Quaternion.Slerp(transform.rotation, targetRot, Time.deltaTime * speed );`

This code must be part of Update, FixedUpdate or a coroutine to work fine.