You can use CSS to make it not display - find the body class of the homepage and do something like:
.home h1 {
display: none;
}
This is only a solution if you are not using any other h1 tags on the homepage, and may also have negative SEO side effects, as it may be perceived by search engines as gaming.
Instead, I recommend editing page.php - or whatever other template file is being applied to your homepage.
Find where the h1 tag is being called, and do something like:
<?php if (!is_home()): ?>
your h1 line goes here
<?php endif; ?>
What this code does is says - if the page is not the homepage, then display the h1 heading.
Reference: WordPress Conditional Tags