At 10.30, the stock was trading at 112 pence, up 12 per cent on the placing price of 100 pence.
Eland raised £118 million, giving the company an initial market value of £135 million.
The proceeds will be used to meet the outstanding balance on the acquisition of a 45 per cent stake in block OML 40, in the Niger Delta, which was jointly owned by Shell, Total and ENI.
The cost of the stake is £97 million (US$154 million) and the remainder of the block is owned by the the Nigerian National Petroleum Corporation.
Together with local partner Starcrest, Eland plans to have OML 40 producing 2,500 barrels of crude a day within six months. The block has proven oil reserves of 71.5 million barrels.
As well as the cash raised from the IPO, the company has secured a £14 million (US$22 million) debt facility and an equity option agreement with two major shareholders for £10 million each.
Chief executive Les Blair said: "I look forward to updating shareholders and the market as we progress our work programme which is designed to rapidly monetise this asset for the benefit of both our shareholders, the communities within the licence area and all other stakeholders."
In its IPO document this morning, Eland also outlined some very aggressive exploration plans targeting 113 million barrels of oil in 2013.
This will be prelude to increasing the company’s production, which is targeted to rise a gross 50,000 barrels a day within four years.
The company is also on the lookout for “under-exploited upstream assets” in Nigeria.
Shell said in June it was seeking buyers for OMLs 30, 34 and 40.
London listed Heritage Oil snapped up OML 30 in a £540 million deal in July.
Meanwhile, Blair was cited in a recent article as saying Eland could be a potential bidder for other assets in Nigeria.