Why the starting current of motor is very high ?

Motor Current is directly proportional to slip (Synchronous speed - Actual speed of Rotor). At the time of start up, rotor is at rest and slip is maximum which results in greater current. when the motor gains speed, the slip decreases and hence the current also decreases.

Most of industrial motors are induction type, which is similar to transformer. The stator winding is primary and rotor winding is the secondary winding. When rotor is at rest, the magnetic field produced by stator winding rotates at synchronous speed and maximum magnetic lines are cut by the stationary rotor winding which results in greater secondary current(load) and hence requires greater current in primary (stator winding). As the rotor speeds up, the no. of magnetic lines cut by rotor (secondary) winding decreases and hence decreases current in stator (primary) winding.

its because the rotor in starting is at rest, off course anything at rest if somebody try to move it you need a large initial force to start it moving.

the starting of induction motors are differed,the motors phenomino is like transformer,at the time of starting the currrent depends up on torque,connected load,and starting gear.

For the principle of magnetic induction the motor stator and rotor windings is synonymous to transformer primary and secondary windings. If you will consider a transformer with the secondary winding is shorted and this is equivalent to a locked rotor condition for a motor, at that moment the primary instantaneous current of that transformer is very high like the starting current of the motor. So current is very high upon motor starting because the rotor is at still like its held as "locked rotor" conditon. 

Due to inertia of the rotor parts.