This functionality not available by default in Magento. I have used the below solution.
You can call this event checkout_cart_product_add_after in the observer.

File Path app/code/local/{namespace}/{yourmodule}/etc/config.xml

<config>
    ...
    <frontend>
        ...
        <events>
            <checkout_cart_product_add_after>
                <observers>
                    <unique_event_name>
                        <class>{{modulename}}/observer</class>
                        <method>overridePrice</method>
                    </unique_event_name>
                </observers>
            </checkout_cart_product_add_after>
        </events>
        ...
    </frontend>
    ...
</config>

And then create an Observer class in this file app/code/local/{namespace}/{yourmodule}/Model/Observer.php

<?php
    class <namespace>_<modulename>_Model_Observer
    {
        public function overridePrice(Varien_Event_Observer $observer)
        {
            // Get the quote item
            $item = $observer->getQuoteItem();
            // Ensure we have the parent item, if it has one
            $item = ( $item->getParentItem() ? $item->getParentItem() : $item );
            // Load the custom price
            $price = $this->_getPriceByItem($item);
            // Set the custom price
            $item->setCustomPrice($price);
            $item->setOriginalCustomPrice($price);
            // Enable super mode on the product.
            $item->getProduct()->setIsSuperMode(true);
        }
        
        protected function _getPriceByItem(Mage_Sales_Model_Quote_Item $item)
        {
            $price;
            
            //use $item to determine your custom price.
            
            return $price;
        }
        
    }
?>