The phrase "becoming suspicious" is grammatically correct and can be used in written English.
It is often used to describe the process of someone starting to feel or think that something is not right or that someone is not being truthful. Example: As she listened to his explanation, she couldn't help but feel herself becoming suspicious of his story.
By spring 2008, the staff were becoming suspicious.
Torontonians are also becoming suspicious of each other.
She eventually took £1.1m from the couple's accounts without them ever becoming suspicious.
"One officer near the walkthrough gate stopped the man after becoming suspicious of him," Shehzad said.
True, it hadn't popped up unsolicited on her News Feed; she had gone Googling after becoming suspicious.
To have my privacy taken away from me — especially by the government — is disturbing, and halting my computer usage seems better than anyone becoming suspicious of me.
She is shown to be fiercely protective of her marriage to Victor, becoming easily suspicious and jealous, for example, of a Dutch marionette that Victor becomes occupied with repairing in the episode "Hole in the Sky", eventually leading her to destroy it.
The counter-argument is that they entrench management, discourage takeover attempts and depress the share price.Shareholders are becoming more suspicious of poison pills.
Meanwhile, there are continuing signs that banks are becoming increasingly suspicious of each others' creditworthiness and are reluctant to lend to each other.
At a time when academic historians were becoming increasingly suspicious of "grand narratives", he saw how important it was to understand the broader forces of historical change.
Irresponsible hyperbole about "chilling" levels of sexual "sadism", rife not just in inner-city gangs but "affluent middle class areas" and "church schools", can only lead to paranoid parents becoming destructively suspicious of every innocent teen romance.
