This paper proposes a novel compact MIMO antenna which has miniaturized radiators and their row correlation coefficient, working for the LTE mobile communication, and its SAR is observed. Each of the proposed radiators has a shape of staircase and the bandwidth is twice larger than the conventional PIFA as 600MHz(21%) in 2.5 GHz - 3.15 GHz. And the area of the radiators is $16.5mm{ imes}9.7mm$ proper for a handheld device. Also, by adding a planar mushroom decoupling structure between the radiators, the isolation is improved. The design has been carried out using the commercial full-wave time-domain EM solver and the finalized MIMO antenna has the return loss less than -10 dB in the LTE band, the isolation better than 20 dB and the efficiency more than 90% with the gain of 4.3 dB. Regarding the SAR of the antenna, it is observed that the average SAR value of 1g is estimated as 1.37W/Kg, which is lower than the SAR standard.