Nearly 130 countries, including many of the world's poorest, are being represented at the meeting in a stadium in the central Bolivian city of Cochabamba.
Morales was fiercely opposed to last December's Copenhagen Accord calling it non-binding.
Instead of gathering top diplomats and world leaders, the Bolivian alternative summit is made up of indigenous groups, scientists, activists and delegations from lower income countries.
The Inter-American Development Bank (IADB) said that the summit would look at new approaches to climate change.
"I believe that the international community is putting in all efforts to reach a global agreement on climate change," Juan Pablo Bonilla, head of the IADB, said from Washington.
"Different areas will be discussed in Bolivia, such as adaptation and the transfer of technology, which of course will result in some important input on the issue."
Opening the summit the Bolivian president said that poor countries would likely bear the brunt of climate change and that all countries should be held accountable for their actions.
Morales also called for the death of careless capitalism so that the Earth can live.
"Either capitalism dies, or it will be Mother Earth," he said to around 20,000 people at the summit.
"We're here because industrialised countries have not honoured their promises."
Copenhagen not clear
Critics say the Copenhagen Accord which seeks to limit a rise in average world temperatures to below 2 degrees Celsius over pre-industrial times does not specify how this goal will be reached.
Developing nations have resisted a legally binding climate treaty, arguing that wealthy nations must bear the primary responsibility for climate change.
The Bolivia summit comes after a preparatory meeting between representatives from the world's leading economies in Washington ahead of the December UN summit in Cancun, Mexico.
The US-led Major Economies Forum comprises 17 countries responsible for the bulk of global emissions, but excludes smaller and poorer nations.
Morales is planning to propose a world referendum this week to ask up to two billion people how they think governments should tackle climate change, and organisers plan to take the final text drafted at the summit to Cancun.
The end of the summit is planned to coincide with Earth Day which is marked throughout most of the world on Thursday, April 22.