The housing authority is building 28 units on the plot of land just off Washington Street West within a stone's throw of Littlepage.
The $7 million project, which includes the cost of acquiring the property and installing infrastructure, should be completed by the end of 2013, Taylor said.
This project, once completed, will be dubbed The Greystone, he said.
Plans are eventually to demolish the 108 units at Littlepage and replace them with new units such as those currently under construction on Washington Street West.
However, the upgrade to the public housing stock does not come without some consequences, the Rev. Matthew Watts believes.
"I applaud Charleston-Kanawha Housing for what they're doing to upgrade the housing in the West Side," said Watts, founder of HOPE Community Development Corp.
"My only concern is there is still a significant concentration of public housing in areas like the West Side."
Such concentration can mean many low-income students attending the same school.
"When the concentration of poverty is high in a single school, you see a decline in the academic performance within the children of that school," Watts said. "That's not the fault of anyone with Charleston-Kanawha Housing; it's just that these unintended consequences do occur."
Taylor disagrees, saying the authority is not increasing the population in the area and is instead building new units to replace the old.
"I would agree with him (Watts) if we weren't getting rid of Littlepage Terrace," Taylor said. "But we're just replacing existing housing with better quality housing.
"We're not really bringing new people in," he added. "We're serving the people that are already here."
Once the original Littlepage buildings are demolished, 49 new housing units will be built on that site, he said.
"We're going to be really busy in the next three or four years," he said.
The number of public housing units in the city has decreased since 2005, Taylor said. That year, there were 1,440 public housing units in Charleston.
In 2012, that number had dropped to 1,271.