1) Copy over app/code/core/Mage/Adminhtml/Block/Catalog/Product/Grid.php 

to app/code/local/Mage/Adminhtml/Block/Catalog/Product/Grid.php

2) add the code below in app/code/local/Mage/Adminhtml/Block/Catalog/Product/Grid.php inside/under

_prepareCollection()

AFTER

->addAttributeToSelect('type_id');

and before

if (Mage::helper('catalog')->isModuleEnabled('Mage_CatalogInventory'))

CODE: 

$collection->joinTable( 'cataloginventory/stock_item', 'product_id=entity_id', 

array("stock_status" => "is_in_stock") )->addAttributeToSelect('stock_status');

3) add the below in in same file _prepareColumns()

    $this->addColumn('stock_status',

    array(

           'header'=> 'Stock Status',     //this is the title of the column

           'width' => '60px',                   // this is the width of the column

           'index' => 'stock_status',

           'type'  => 'options',

           'options' => array('1'=>'In Stock','0'=>'Out Of Stock'),

    ));

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