Dear Dinesh,

Yes, after AMIE degree, you are eligible for GATE examination.

As per GATE eligiblity crieteria, if a candidate has cleared examinations conducted by following professional societies / institutions:

• AMIE
  
• AMICE
  
• The Institution for Engineers India (IE)
  
• The Institution for Civil Engineers India (ICE)
• The Institution for Electronics and Telecommunication Engineers India (IETE)
• The Aeronautical Society of India (AeSI)
  
• The Indian Institute of Chemical Engineers, including Polymer and Environmental Group
  (IIChemE)
• The Indian Institute of Metals (IIM)
• The Indian Institute of Industrial Engineers (IIE)
  

The degree is equilavent to B.Tech degree from any of the UGC/AICTE recognised institute of India.

Not only GATE, you are eligible for most of the goverement exams like UPSC-ESE (Engineering Services Examination), UPSC CSE (Civil Services Examination), and other govt. jobs where B.Tech is the requirement.

You can check out GATE 2019 information brochure here:

Hope this helps.