Agnes Renwick (86) of Pendreich Avenue, was struck by a car while crossing Lothian Street, close to its junction with Waverley Crescent, at midday on Wednesday, November 26.
She died eight days later in Edinburgh Royal Infirmary as a result of he
r injuries.
Her family believe the lack of a pedestrian crossing was a "major factor" in her accident and has called on Midlothian Council to improve road safety for pedestrians in the area.
The scene of the accident has two busy junctions with Waverley Crescent and Eldindean Road, two bus stops, a public house, a newsagents as well as a number of small businesses.
Mrs Renwick's youngest son Jim told The Advertiser: "There is a need for a pedestrian crossing of some sort. There is no provision on that stretch from Eldindean to Bonnyrigg Toll.
"It is an extremely busy road in the area where my mother was struck by the vehicle. I have an elderly aunt and uncle who also cross that road every day.
"They are extremely concerned with there being no provision for safe crossing. It is putting other people's lives are risk."
Mr Renwick added that Eskbank Road, which continues on from Lothian Street towards Eskbank, has a pedestrian crossing and a number of traffic islands.
The family would also like to see the bus stop, on the Waverley side of the road, moved closer to Bonnyrigg town centre.
"Even if we had a refuge in the middle of the road that would be better than nothing," said Mr Renwick.
Midlothian Council Leader Derek Milligan said, after being approached by the Renwick family, he had asked the strategic services director and transport frontline services manager to look at the situation "as a matter of urgency".
"We are currently having a look to see what measures can be put in place here," he added.
Mrs Renwick, who had three sons, five grandchildren and four great-grandchildren, worked for many years as the cashier at the town's Co-op store before joining Bonnyrigg Post Office.
She retired as a volunteer at the Dalkeith cancer research charity shop six weeks before the accident.