The world's largest democracy is India, and as such, it is not unreasonable to assume that this is the world's largest election. In 2009, for example, the total vote count was 714 million which is larger than that of the United States and EU combined.
In a fashion similar to that of the United States President, the President of India is indirectly elected through electors, but if the President of the United States can be said to be elected "by the people" (and indeed, there are vote tallies that often show how many people "voted for the candidate"), then the same can be said of the President of India. In 2012, there were over 700,000 electoral votes (compared to 538 in the United States) cast for Pranab Mukerjee and another 300,000 for his closest rival. Each of these electors is traceable to the will of 1,000 residents in each state, meaning that over a billion people are represented.
That said, since the question directly excludes electors, we need move on to the Lok Sahba. In 2009, Manmohan Singh's Congress Party received over 153 million votes in a three-way election that the United Kingdom's Guardian called the "world's largest democratic poll". The election itself was 28 days long and involved nearly 700 million voters. In a party based system, the choice of party could be considered tantamount to choosing its leader, so may or may not fall within the scope of the question.
That all said, with only 543 seats in the Lok, there is bound to be a single constituency within that body that would almost certainly take the prize. In contrast to China, its logical rival, which has 2,987 members in its parliment and is of dubious democratic value, the sheer number of members (4 times the members, similar sized electorate) dictates that each seat in India would have the most direct electors per position.