Wakefield Council has approved the application which is designed to increase capacity at Capri Café Lounge.
The scheme received one objection from a resident living close to the business on Leeds Road, next to Newton Hill roundabout.
It was claimed the extension would lead to a loss of privacy for those living next to the site.
Concerns were also raised about noise coming from the business.
The café is a recent addition to the site which has been built beside the main Capri restaurant.
A report into the extension proposal states: “The proposed extension and roof terrace would provide for additional capacity, menu diversity and operation efficiency.
“The café building would continue to provide a place for having a coffee and associated breakfast and lunch menus, in addition to the main use of the site as a restaurant.”
A neighbour’s objection to the plans state: “If developed, any prospective customers will have a clear view of items within our property, such as vehicles and garden furniture, which could potentially cause security issues.
“Since the original development of this café bar opened six to 12 months ago, we have experienced a significant increase in noise from the site.
“The development has created an enclosed area at the rear which retains noise such as car engines, doors opening and closing, banging, people shouting and laughing, music playing, all quite late into the evening up to midnight and is a regular occurrence.
“We feel we have been extremely tolerant of the previous developments and rapid business expansion at the site up to now.
“But this is a step too far and will affect our privacy and quality of life.”
The original planning application was amended to include a landscaped “green wall” to reduce the impact on neighbouring homes.
The report adds: “The proposed ‘green wall’ will assist in diffusing noise and glanced views towards the closest property from customers.
“It is not considered that residential amenity would be compromised.”
The roof terrace will be allowed to be in use between 7.30am and 2.30pm, Monday to Saturday, and 8am to 2pm on Sundays and bank holidays.