How to pursue a Psychology career in academia from non-Psychology background? I don't have a Psychology degree but would like to pursue it. I'm interested in academic related work, teaching and research. 

Is there any way I could make a career change without taking another Bachelor's degree?
Psychology is a very broad field. While some subfields require a license  (e.g., clinical psychology), a huge number of undergraduate fields can prepare you for academic related work, teaching and research. I know individuals with Bachelors in Math, Physics, BME, EE, CS, MechE, Statistics, Neuroscience, Biology, Chemistry, Sociology, Speech and Hearing, Music, and Education who have either gone on to get a PhD in Psychology or a faculty position in a Psychology Department.

As a former faculty member in a Psychology department with an engineering background, I cannot think of any major I would turn away out of hand for a PhD position.