Yes. You are eligible to appear for GATE Exam as you have completed your B.Tech course.

Here I am providing you the eligibility criteria for GATE Exam.

Academic Qaulification :
-One should have completed Graduation in Engineering to appear for GATE Exam.
-Even the candidates who are in final or pre final year of Engineering are also eligible to appear for GATE Exam.

Age limit : -
There is no minimum and maximum age limit to appear for GATE Exam

Number of attempts :
-There is no limit on the number of attempts for GATE Exam.
-One can appear for GATE Exam for any number of times.

GATE score card is valid for a period of 2 years in the sense if a candidate has appeared for GATE Exam in 2 consecutive years, he can use any of the score card of the 2 years to get admission to MCA course.


Source: http://entrance-exam.net/forum/general-discussion/can-i-appear-gate-exam-having-completed-3years-b-tech-after-completion-diploma-352968.html#ixzz5DQ9XAeuF