The Black Stars had to fight to defeat DR Congo 2-1 in the quarter-final to be able to advance to the last four of the competition in Gabon.
Brothers Jordan and Andre Ayew scored as Ghana beat a spirited Leopards in Oyem to reach the semi-finals on Sunday.
Ghana will have an extra day to rest and plot victory over Cameroon in Franceville on Thursday having reached the last four for the sixth time in a row.
Grant says the Black Stars must not expect the Cameroonians to be pushovers in their match on Thursday.
‘I saw the Cameroonians yesterday [Saturday] and they were very good, a very tough side,” Grant told Pulse Ghana.
“In the group stage they played well and against Senegal they were very impressive. Senegal created more chances but i think Cameroon deserved to beat win the match.
“The semi final is going to be tough.”
Ghana were delighted for quarter-final victory and all the goals in their quarter-final with DR Congo came in a 15-minute spell in the second half.
Ghana were ahead when Mubarak Wakaso picked out Jordan Ayew and he sprinted to the edge of the box before unleashing a fierce shot past Congolese goalkeeper Ley Matampi.
It was a goal of high quality, but the equaliser from Paul-Jose Mpoku was even better as the Panathinaikos winger took aim from 30 metres and found the top corner of the net.
Congo were the architects of their own downfall after that though as defender Joyce Lomalisa clumsily fouled Christian Atsu in the box and Andre Ayew converted the penalty.
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