This is a regular verb. It follows the conjugation pattern of the verb hablar.
PresentPresente
Yo sospecho que va a llover esta tarde.
I suspect it is going to rain this afternoon.
ImperfectPretérito imperfecto
Nadie sospechaba nada de la fiesta sorpresa.
Nobody suspected anything about the surprise party.
PreteritePretérito indefinido
El detective sospechó del vecino desde el principio.
The detective suspected the neighbor from the start.