The Skinny Direct model has been designed to beat prepay churn, Parker says.
"We want happier customers who stay longer with us because the traditional prepay model is one of high churn ... That's something we're keen to change."
Parker says company research has shown customers want to be able to take care of their phone bill online and on mobile.
"The happiest ones are the ones that self-serve, look after themselves, and top up online and on the app.
"Telcos have been selling online for a while but we've all struggled to breakthrough the barrier to turn a telco into an online and mobile experience."
Parker said he was pleased Skinny had over 200,000 active users after it launched four years ago.
Parker said he imagined competitors like 2 Degrees and Vodafone would also be looking to offer a completely online model.